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Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : KNM [1]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

A train accelerating uniformly from rest attains a

(A) (B) (C) (D)

maximum speed of 40 ms 1 in 20 s. It travels at this speed for 20 s and is brought to rest with uniform retardation in further 40 s. What is the average velocity during this period.

2.

(A)

80 / 3 ms 1

(B)

25 ms 1

(C)

40 ms 1

(D)

30 ms 1

3.

The graph below represents motion of a car. The displacement of the car in 20 s is : (A) (B)

4.

5.

6.

Two balls are dropped to ground from different heights. One ball is dropped 2 s after the other but the first ball hits the ground in 5 s, then, the difference in their heights is : (A) 125 m (B) 45 m (C) 80 m (D) 170 m

7.

A body starts from rest, with uniform acceleration a. The acceleration of a body as function of time t is given by the equation a = pt where p is constant, then the displacement of the particle in the time interval t = 0 to t = t1 will be.

On displacement-time graphs, two straight lines make angle 60 and 30 with time axis. The ratio of the velocities represented by them is : (A) 1:2 x(m) (B) 1:3 A (C) 2:1 60 30 t(s) (D) 3:1 O B C

20 m

(C)

90 m

(D)

10 m

8.

v(ms 1)

60 m

8 12

16 20

9.

Two particles A and B get 4m closer each second while traveling in opposite direction. They get 0.4 m closer every second while traveling in same direction. The speeds of A and B are respectively.

2.2 ms 1 and 0.4 ms 1

(B)

2.2 ms 1 and 1.8 ms 1

(C)

4 ms 1 and 0.4 ms 1 (D)

10. None of the above

A car is moving on a road and rain is falling vertically. Select the correct answer :

VMC/Kinematics of a Particle

1 3 pt 2 1

(B)

1 2 pt1 3

(C)

1 2 pt1 4

(D)

1 3 pt 6 1

A train starts form station with an acceleration 1ms 2 has

doubled? (A) 8s (C) 12 s

t(s)

–10

(A)

(A)

a velocity of 100 ms 1 . In what time, the velocity will be

10 4

The rain will strike the hind screen only The rain will strike the front screen only The rain will strike both the screens The rain will not strike any of screens

54

(B) (D)

10 s 14 s

A particle moves 200 cm in the first 2 s and 220 cm in the next 4 s with uniform deceleration. The velocity of the particle at the end of 7s is : (A)

12 cms 1

(B)

11 cms 1

(C)

10 cms 1

(D)

5 cms 1

The acceleration of a particle increases linearly with time t as 6t. If the initial velocity of the particle is zero and the particle starts from the origin, then the distance traveled by the particle in time t will be : (A) t (B) t2 3 (C) t (D) t4

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : KNM [2]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

2.

3.

A car starts from station and moves along the horizontal road by a machine delivering constant power. The distance covered by the car in time t is proportional to : (A) t2 (B) t3/2 2/3 (C) t (D) t3

7.

The displacement of a particle undergoing rectilinear motion along the x-axis is given by x = (2t2 + 21t2 + 60t + 6). The acceleration of the particle when its velocity is zero is : (A)

36 ms 2

(B)

9 ms 2

(C)

9 ms 2

(D)

18ms 2

7 ms 1

(C)

6 ms 1

(D)

5 ms 1

A particle is moving on a straight line path with constant acceleration directed along the direction of instantaneous velocity. Which of the following statements are false about the motion of particle? (A) Particle may reverse the direction of motion

(C) (D) 8.

second and vt in ms . The acceleration of the particle when it is 2 m from the origin is : (A)

28 ms 2

(B)

22 ms 2

(C)

12 ms 2

(D)

10 ms 2

A particle moving along a straight line has a

9.

A particle is moving with constant initial velocity 4 ms 1 10.

till t = 1.5 s. Then it accelerates at 10 ms 2 till t = 3. The distance covered is : (Take g 10 ms 2 ) (B) (D)

36.25 m 23.45 m

A car travels equal distances in the same direction with velocities 60 kmh 1 , 20 kmh 1 and 10 km h 1 respectively. The average velocity of the car over the whole journey of motion is :

VMC/Kinematics of a Particle

2

1 n

(D)

2 1 n n2

The velocity-time relation of an electron starting from rest is given by v = kt where k 2 ms 1 . The distance traversed in first 3 s is : (A) 9m (B) 16 m (C) 27 m (D) 36 m

When its velocity is 1ms 1 , its acceleration (in ms 2 ) is : (A) 1 (B) 2 (C) 7 (D) 0.5

17.25 m 40 m

2 n

These two are connected by the relation v 49 y .

(A) (C)

Distance covered is not equal to magnitude of displacement the magnitude of average velocity is less than average speed All of the above

A body starts from rest and moves with a constant acceleration. The ratio of distance covered in the nth second to the distance covered in n second is : 2 1 1 1 (A) (B) 2 n n n2 n (C)

velocity v ms 1 , when it cleared a distance of y metre.

6.

(B)

A body starts from origin and moves along x-axis such 1

5.

8 ms 1

(B)

that at any instant velocity is vt 4t 3 2t where t is in

4.

(A)

55

Which of the following statements is correct? (A) When air resistance is negligible, the time of ascent is less than the time of descent (B) When air resistance is not negligible, time of ascent is less than the time of descent (C) When air resistance is not negligible, the time of ascent is greater than the time of descent (D) When air resistance is not negligible, the time of ascent is lesser than the time of descent

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : KNM [3]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

: TIME TAKEN

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

A 2 m wide truck is moving with a uniform speed v0 8 ms 1 along a straight horizontal road. A pedestrian starts to cross the road with a uniform speed v when the truck is 4 m away from him. The minimum value of v, so that he can cross the road safely is : (A)

2.

4.

(B)

4.6 ms 1

3.57 ms 1

(C)

1.414 ms 1

(D)

A bus moves over a straight level road with a constant acceleration a. A body in the bus drops a ball outside. The acceleration of the ball with respect to the bus and the earth are respectively. (A)

3.

2.62 ms 1

a and g

(B)

a g and g a

a 2 g 2 and g (D)

(C)

a 2 g 2 and a

Two cars move in the same direction along parallel roads. One of them is a 100 m long traveling with a velocity of 7.5 ms 1 . How long will it take for the first car to overtake the second car? (A) 24 s (B) 40 s (C) 60 s (D) 80 s A car is moving along a straight road with uniform acceleration. It passes through two points P and Q separated by a distance with velocities 30 kmh 1 and 40 kmh 1 respectively. The velocity of car midway between P and Q is : (A)

5.

33.3 kmh 1

(B)

1 kmh 1

25 2 kmh 1

(C)

(D)

35.35 kmh 1

A particle starts from the origin and moves along the X-axis such that the velocity at any instant is given by 4t 3 2t , where t is in second and velocity is in ms–1. What is the acceleration of the particle when it is 2 m from the origin? (A)

10 ms 2

(B)

12 ms 2

22 ms 2

(C)

(D)

28 ms 2

–1

6.

The driver of a car moving with a speed of 10 ms sees a red light ahead, applies brakes and stops after covering 10 m distance. If the same car were moving with a speed of 20 ms–1, the same driver would have stopped the car after covering 30 m distance. Within what distance the car can be stopped if traveling with a velocity of 15 ms–1? Assume the same reaction time and the same deceleration in each case. (A) 18.75 m (B) 20.75 m (C) 22.75 m (D) 25 m

7.

If the velocity of a car is increased by 20%, then the minimum distance in which it can be stopped increases by : (A) 44% (B) 55% (C) 66% (D) 88%

8.

If the velocity v of a particle moving along a straight line decreases linearly with its displacement s from 20 ms–1 to a value approaching zero at s = 30 m, then acceleration of the particle at s = 15 m is : 2 2 2 ms ms 2 (A) (B) 3 3 20 2 20 2 ms ms (C) (D) 3 3

9.

V

(in ms 1 ) s (in m)

30

For a particle moving in a straight line, the displacement of the particle at time t is given by S t 3 6t 2 3t 7 . What is the velocity of the particle when its acceleration is zero? (A)

10.

20

9 ms 1

(B)

12 ms 1

3 ms 1

(C)

The displacement x of a particle at the instant when its velocity v is given by v (A)

1.5 units, 4 units

VMC/Kinematics of a Particle

(B)

3 units, 4 units

(C)

(D)

3x 16 . Its acceleration and initial velocity are

16 units, 1.6 units (D)

56

42 ms 1

16 units, 3 units

HWT/Physics

Vidyamandir Classes DATE :

IITJEE :

TIME : 25 MINUTES

MARKS : 10

NAME :

TEST CODE : KNM [4]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

: TIME TAKEN

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

A particle is moving with uniform acceleration along a straight line. The average velocity of the particle from P to Q is 8 ms 1 and that from Q to S is 12 ms 1 . If QS = PQ, then the average velocity from P to S is : (A)

9.6 ms 1

(B)

12.87 ms 1

64 ms 1

(C)

(D)

O P Q S

327 ms 1

2.

A particle starts from rest and travels a distance s with uniform acceleration, then it travels a distance 2 s with uniform speed, finally it travels a distance 3 s with uniform retardation and comes to rest. If the complete motion of the particle in a straight line then the ratio of its average velocity to maximum velocity is : (A) 6/7 (B) 4/5 (C) 3/5 (D) 2/5

3.

A particle moving in a straight line with uniform acceleration is observed to be a distance a from a fixed point initially. It is at distance b, c, d from the same point after n, 2n, 3n second. The acceleration of the particle is : c 2b a cb a c 2b a cba (A) (B) (C) (D) n2 9n 2 4n 2 n2

4.

A particle moves in a straight line so that its displacement x metre at time t second is given by t time t second is : (A)

1 x

5.

(B)

t2 x

3

1 t2 x x3

(C)

(D)

v1v2 v1 v2

(B)

2v1v2 v1 v2

3v1v2 v1 v2

(C)

(D)

1 x2

zero

6 + 4t = 0.2t2

Two cars leave one after the other and travel with and acceleration of 0.4 ms 2 . Two minutes after the departure of the first car, the distance between them becomes 1.90 km. The time interval between their departures is : (A) 50 s (B) 60 s (C) 70 s (D)

8.

x3

A man runs at a speed of 4 ms 1 to overtake a standing bus. When he is 6 m behind the door at t = 0, the bus moves forward and continues with a constant acceleration of 1.2 ms 2 . The man reaches the door in time t. Then, (A) 4t = 6 + 0.6 t2 (B) 1.2t2 = 4t (C) 4t2 = 1.2 t (D)

7.

t2

Three particles start from the origin at the same time, one with a velocity v1 along x-axis, the second along the y-axis with a velocity v2 and the third along x = y line. The velocity of the third so that the three may always lie on the same line is : (A)

6.

3

x 2 1 . Its acceleration in ms–2 at

80 s

The engine of a train can impart a maximum acceleration of 1 ms 2 and the brakes can give a maximum retardation of 3 ms 2 . The least time during which a train can go from one place to the other place at a distance of 1.2 km is nearly. (A) 108 s (B) 191 s (C) 56.6 s (D) time is fixed

VMC/Kinematics of a Particle

57

HWT/Physics

Vidyamandir Classes 9.

The acceleration of a particle increasing linearly with time t is bt. The particle starts from the origin with an initial velocity v0. The distance traveled by the particle in time t will be : 1 1 1 1 v0t bt 3 v0t bt 2 v0t bt 3 v0t bt 2 (A) (B) (C) (D) 6 3 3 3

10.

In the given v-t graph, the distance travelled by the body in 5s will be : (A) 20 m (B) 40 m (C) 80 m (D) 100 m

VMC/Kinematics of a Particle

58

40 30 20 V (in ms 1 ) 10 0 –10 –20

2

3

4

5

time (in sec)

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : KNM [5]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

: TIME TAKEN

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking.

2.

3.

Figure gives the speed - time of the motion of a car. What is the ratio of the distance traveled by the car during the last two seconds to the total distance traveled in seven seconds ? (A) 1/9 (B) 2/9 (C) 1/3 (D) 4/9

12 ms 1

14ms 1

(C)

10 5

16ms 1

(D)

m1u m2

(B)

m2u m1

m1 m2 m1 m2

(C)

The displacement y (in meters) of a body varies with time t (in seconds) as y

(C)

(D)

u

2 2 t 16t 2 3

12 seconds

(D)

16 seconds 30

The velocity – time graph of a stone thrown vertically upward with an initial velocity of 30ms 1 is shown in the figure. The velocity in the upward direction is taken as positive and that in the downward direction as negative. What is the maximum height to which the stone rises? (A) 30 m (B) 45 m (C) 60 m (D) 90 m

7.

15

Two balls of mass m1 and m2 are thrown vertically upward with the same speed u. If air resistance is neglected, they will pass through their point of projection in the downward direction with a speed :

How long does the body take to come to rest? (A) 8 seconds (B) 10 seconds 6.

B

The acceleration of (in ms 2 ) of a body, starting from rest varies with time t (in s) according to the relation a 3t 4 . The velocity of

(A) 5.

A

E C D 1 2 3 4 5 6 7 Time (s) A stone falls from rest. The distance covered by the stone in the last second of its motion equals the distance covered by it during the first three seconds of its motion. How long does the stone take the reach the ground ? (A) 4s (B) 5s (C) 6s (D) 9s

the body at time t = 2s will be: (A) (B) 10ms 1 4.

25 20

Velocity (ms–1)

1.

Speed (ms–1)

Choose the correct alternative. Only one choice is correct.

A

20 10 B 10

1 2

3

Time (s) 4 5

6

20 30

C

1

At t = 0, an arrow is fired vertically up-wards with a speed of 98ms . A second arrow is fired vertically upwards with the same speed at t = 5s. Then: (A) the two arrows will be a the same height above the ground at t = 10s (B) the two arrows with reach back their staring point at t = 20 s and at t = 30s (C) the ratio of the speeds of the first and the second arrows at t = 20s will be 2 : 1 (D) the maximum height attained by either arrow will be 980 m

VMC/Kinematics of a Particle

59

HWT/Physics

Vidyamandir Classes 8.

The area under the velocity – time graph between any two instant t t1 and t t2 gives the distance covered in time t t2 t1 (A) Only if the particle moves with a uniform velocity (B) only if the particle moves with a uniform acceleration (C) Only if the particle moves with an acceleration increasing at a uniform rate (D) In all case irrespective of whether the motion in one of uniform velocity, or of uniform acceleration or of variable acceleration.

9.

Which of the following statement is wrong? (A) If speed of a particle changes, its velocity must change. (B) If velocity of a particle doesn’t change, its speed must remain constant (C) If speed of a particle doesn’t change, its velocity must remain constant (D) If velocity of a particle changes, its speed may or may not change

10.

The variation in the speed of a car during its two hour journey is shown in the graph of Figure. The magnitude of the maximum acceleration of the car occurs during the interval. (A) OA (B) BC (C) CD (D) DE

VMC/Kinematics of a Particle

60

100 80 60 40 20

E C D

A B 0.5

1.0 1.5 2.0

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : KNM [6]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

: TIME TAKEN

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct 1.

A parachutist drops freely from an aeroplane for 10s before the parachute opens out. Then he descends with an net retardation of 2.5ms 2 . If he bails out of the plane at a height of 2495 m and g = 10ms 2 , his velocity on reaching the ground will be : (A)

2.

(B)

7.5 ms 1

5 ms 1

(C)

(D)

10ms 1

A car accelerates from rest at a constant rate for some time after which it decelerates at a constant rate to come to rest. If the total time elapsed is t, the maximum velocity acquired by the car is given: (A)

3.

2.5 ms 1

t

(B)

t

(C)

2 2 t

(C)

1 2 2 2 t (D) 2

(D)

2 t

The distance traveled by the car in Q 2 above is given by : (A)

1 2 t 2

(B)

1 2

2 t

1 1 2 2 t 2

4.

Water drops fall at regular intervals from a roof. At an instant when a drop is about to leave the roof, the separations between 3 successive drops below the roof are in the ratio: (A) 1:2:3 (B) 1:4:9 (C) 1:3:5 (D) 1 : 5 : 13

5.

A freely falling body, falling from a tower of height h covers a distance h/2 in the last second of its motion. The height of the tower is (Take g = ms–2) nearly (A) 58 m (B) 50 m (C) 60 m (D) 55 m

6.

Ball A is rolled in a straight line with a speed of 5ms–1 towards a bigger ball B lying 20 m away. After collision with ball B, ball A retraces the path and reaches its starting point with a speed of 4ms 1 . What is the average velocity of ball A during the time interval 0 to 6s? (A) zero (B) 2 ms–1 (C) 4 ms–1 (D) 5 ms–1

7.

A train moving southwards at a speed of 30ms 1 . A monkey is running northwards on the roof of the train with a speed of 5ms 1 . What is the velocity of the monkey as observed by a person standing on the ground? (A)

35ms 1 in the southward direction

(B)

(C)

25ms 1 in the southward direction

(D)

35ms 1 in the northward direction 25ms 1 in the northward direction –1

8.

A jet airplane traveling from east to west at a speed of 500 kmh ejects out gases of combustion at a speed of 1500 kmh–1 with respect to the jet plane. What is the velocity of the gases with respect to an observer on the ground? (A) 1000 kmh–1 in the direction west to east (B) 1000 kmh–1 in the direction east to west –1 (C) 2000 kmh in the direction west to east (D) 2000 kmh–1 in the direction east to west

9.

A police van moving on a highway with a speed of 36 kmh–1 fires a bullet at a thief’s car speeding away in the same direction with a speed of 108kmh 1 . If the muzzle speed of the bullet is 140 ms–1, with what speed will the bullet hit the thief’s car? (A) 120 ms–1 (B) 130 ms–1 (C) 140 ms–1 (D) 150 ms–1

10.

Two persons P and Q are standing 54 m apart on a long moving belt. Person P rolls a round stone towards person Q with a speed of 9 ms–1 with respect to the belt. If the belt is moving with a speed of 4 ms–1 in the direction from P to Q, what is the speed of the stone with respect to an observer on a stationary platform? (A) 4 ms–1 (B) 5 ms–1 (C) 9 ms–1 (D) 13 ms–1

VMC/Kinematics of a Particle

61

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : KNM [7]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

: TIME TAKEN

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

2. 3.

From the top of a multi-storied building 40 m tall, a body projects a stone vertically upwards with an initial velocity 10ms 1 such that it eventually falls to the ground. After how long will the stone strike the ground? Take g = 10ms 2 (A) 1s (B) 2s (C) 3s (D)

4s

In Q.1 above, after how long will the stone pass through the point from where it was projected ? (A) 1s (B) 2s (C) 3s (D)

4s

In Q.1, what will be the speed of the stone when it strikes the ground ? (A)

4.

10ms 1

(B)

20ms 1

30ms 1

(C)

(D)

40 ms 1

A balloon is rising vertically upwards at a velocity of 10ms 1 . When it is at a height of 45m from the ground, a parachutist bails out from it. After 3 s he opens his parachute and decelerates at a constant rate of 5ms 2 . What was the height of the parachutist above the ground when he opened his portraiture? Take g = 10ms 2 (A) 15 m (B) 30 m (C)

45 m

(D)

60 m

5.

Two identical balls are shot upward one after another at an interval of 2 s along the same vertical line with same initial velocity of 40 m/s. The balls collide after ns the first ball is shot. What is the value of n? (A) 2 (B) 3 (C) 4 (D) 5

6.

Water in a well is at a depth h. A ball is released from ground so that it falls, into the well. The speed of sound in air is c. The time after which sound of splash is heard is : (A)

7.

2h h g 2c

(C)

(D)

h h g c

3kmh 1

(B)

6kmh 1

9khm 1

(C)

(D)

r O

60

r

12kmh 1

3 cot 1 with the vertical towards south 4

3 cot 1 with the vertical towards north 4

(D)

A swimmer can swim in still water with a speed of 3ms 1 .While crossing a river his average speed is 5ms 1 . If he crosses the river in the shortest possible time, what is the speed of flow of water? (A)

10.

2h h g c

Rain is falling vertically with a speed of 4ms 1 . After some time wind starts blowing with a speed of 3ms 1 in the north to south direction. In order to protect himself from rain, a man standing on the ground should hold his umbrella at an angle given by: 3 3 (A) tan 1 with the vertical towards south (B) tan 1 with the vertical towards north 4 4 (C)

9.

(B)

A cyclist starts from the centre O of a circular track of radius r = 1 km, reaches the edge P of the track and then cycles along the circumference and stops at point Q as shown in Figure. If the total time taken is 10 min, what is the average velocity of the cyclist? (A)

8.

2h 2h g c

2ms 1

(B)

4ms 1

5ms 1

(C)

(D)

6ms 1

A body starting from rest, moves in a straight line with a constant acceleration a for a time interval t during which it travels a distance s1. If continues to move with the same acceleration for the next time interval t during which it travels a distance s2. The relation between s1 and s2 is : (A) (B) (C) (D) s2 s1 s2 2 s1 s2 3s1 s2 4 s1

VMC/Kinematics of a Particle

62

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : KNM [8]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

: TIME TAKEN

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

A body dropped from the top of a tower hits the ground after 4 s. How much time does it take to cover the first half of the distance from the top of the tower? (A)

2.

3.

4.

(B)

2s

(C)

(D)

2 2s

3s

A body moving in a straight line with constant acceleration of 10ms 2 covers a distance of 40 m in the 4th second. How much distance will it cover in the 6th second? (A) 50 m (B) 60 m (C) 70 m (D) 80 m A body, moving in a straight line with an initial velocity of 5ms 1 and a constant acceleration, covers a distance of 30 m in the 3rd second. How much distance will it cover in the next 2 seconds? (A) 70 m (B) 80 m (C) 90 m (D) 100 m A body, moving in a straight line, with an initial velocity u and a constant acceleration a, covers a distance of 40 m in the 4th second and a distance of 60 m in the 6th second. The value of u and a respectively are: (A)

5.

1s

10ms 1,5ms 2

(B)

10ms 1 10ms 2

5ms 1 5ms 2

(C)

(D)

5ms 110ms 2

A body, starting from rest and moving with a constant acceleration, covers a distance s1 in the 4th second and a distance s2 in the 6th second. The ratio s1 / s2 is: (A)

2/3

(B)

4/9

(C)

6/11

(D)

7/11

6.

A car, starting from rest, has a constant acceleration a1 for a time interval t1 during which it covers a distance s1. In the next time interval t2 the car has a constant retardation a2 and comes to rest after covering a distance s2 in time t2. Which of the following relations is correct? a1 s2 t2 a1 s t a1 s2 t1 a1 s t (A) 1 1 (B) (C) 1 2 (D) a2 s1 t1 a2 s2 t2 a2 s1 t2 a2 s2 t1

7.

In Q.6 if the total distance covered by the car is s, the maximum speed attained by it will be : 1

(A)

a1a2 2 2s . a 1 a2

1

(B)

a1a2 2 2s . a 1 a2

1

s a1a2 2 . 2 a 1 a2

(C)

1

(D)

s a1a2 2 . 2 a 1 a2

8.

A car, starting from rest, is accelerated at a constant rate until it attains a speed v. It is then retarded at a constant rate until it comes to rest. The average speed of the car during its entire journey is: v v v (A) zero (B) (C) (D) 2 2 2

9.

The displacement of a body from a reference point, is given by : Where x is in metres and t in seconds. This shows the body is: (A) at rest (B) accelerated (C)

10.

x 2t 3

decelerated

(D)

in uniform motion

6ms 1

(D)

12ms 1

In Q.9, what is the initial velocity of the body? (A)

2ms 1

VMC/Kinematics of a Particle

(B)

3ms 1

(C)

63

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : KNM [9]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

: TIME TAKEN

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

2.

A car is moving at a certain speed. The minimum distance over which it can be stopped is x. If the speed of the car is doubled, what will be the minimum distance over which the car can be stopped ? (A) 4x (B) 2x (C) x/2 (D) x/4 A bullet is fired vertically upwards with an initial velocity of 50ms 1 . It covers a distance h1 during the first second and a distance h2 during the last 3 seconds of its upward motion. If g 10ms 2 , h1 and h2 will be related as :

3.

4.

h h1 2 3 A ball is thrown vertically downward with a velocity u from the top of a tower. It strikes the ground with a velocity 3u. the time taken by the ball to reach the ground is given by:

(A)

h1 3h2

(B)

h1 2h2

(C)

h1 h2

(D)

(A)

u g

(B)

2u g

(C)

3u g

(D)

4u 2 g

In Q.3, the height of the tower is given by :

5.

u2 2u 3u 4u 2 (B) (C) (D) g g g g A ball is dropped from the top of a building 3.2 m high and it rebounds to a height of 1.8 m. The ball is in contact with the floor for 0.05 s. What is ball’s average acceleration during this period? (Use g = 10 m/s2) (A) 180 m/s2 (B) 280 m/s2 (C) 380 m/s2 (D) 480 m/s2

6.

The distance x covered by a body moving in a straight line in time t is given by the relation

(A)

2 x 2 3x t If v is the velocity of the body at a certain instant of time, its acceleration will be:

v3

(A) 7.

2v3

3v3

(C)

4v3

(D)

The v-x graph for a particle moving along a straight line is shown in the figure. At which of the points marked, the object is slowing down? (A) 1 (B) 3 (C) 1 and 2 (D)

8.

(B)

v 2 3

1

x

t(s)

3 and 2

The body starts from rest at time t = 0 and undergoes an acceleration as shown in Figure. Which of the graphs shown in figure represents the velocity - time (v – t) graph of the motion of the body from t = 0 s to t = 4s) 6 v 3 (ms–1) 0

A C

v 3 (ms–1)

B 1 2 3 t(s) (A)

6

4

VMC/Kinematics of a Particle

0

A

B

D 1 2 3 t(s) (B)

B

6 v 3 (ms–1)

C

0

4

64

6

A 1 2 3 t(s) (C)

C 4

v 3 (ms–1) A 0

B C

D 1 2 3 t(s) (D)

4

HWT/Physics

Vidyamandir Classes 9.

A body, moving in a straight line, covers half the distance with a speed V, the remaining part of the distance was covered with a speed V for half the time and with a speed V for the other half of the time. What is the average speed of the body? (A)

10.

2V V V

2V

V V

(B)

V V V

2V

V V

2V V V V V

(C)

(D)

V V V V V

A car is moving on a straight horizontal road with a speed v. When brakes are applied to give a constant retarding a, the are is stopped in a shortest distance S. If the car wares moving on the same road with a speed 3 v and the same retardation a is applied, the shortest distance in which the car is stopped will be: (A) 3S (B) 6S (C) 9S (D) 27 S

VMC/Kinematics of a Particle

65

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : KNM [10]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

: TIME TAKEN

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

A particle starts from rest at t = 0 and moves in a straight line with an acceleration as shown below. The velocity of the particle at t = 3s is : (A) (B) (C) (D)

2.

2 m/s 3 m/s 4 m/s 6 m/s

4.

3 t(s)

0 1 2

–3

mv 2 2t

v2 2T

(B)

(C)

4

3

v

The velocity-time graph of a body is shown in figure. The slope of the line is ‘m’. The distance travels by body in time Ts (A)

3.

a(m/s)

v

2mv2

(D)

The graph describes an airplane’s acceleration during its take-off run. The airplane’s velocity when it lifts off at t = 20s is: (A) 40 m/s (B) 50 m/s (C) 90 m/s (D) 180 m/s

v2 2m

a(m/s2)

O

t

T

5 3 O

10

20 t(s)

A parachutist jumps out of an aircraft, falls freely for some time and then opens his parachute. Identify the graph which correctly represents his acceleration (a) versus time (t) graph: a a a a

(A)

0

t

(B)

0

t

(C)

0

t

(D)

0

t

For Q.5 - 6 (A) (B) (C) (D)

Statement-1 is True, Statement-2 is True and Statement-2 is a correct explanation for Statement-1 Statement-1 is True, Statement-2 is True and Statement-2 is NOT correct explanation for Statement-1 Statement-1 is True, Statement-2 is False Statement-1 is False, Statement-2 is True

5.

A ball is thrown vertically upwards from ground. At its highest point. Statement 1: Velocity = 0. Statement 2: Acceleration = 0.

6.

A particle is in uniform motion. Statement 1: For the particle v-t graph is a straight line parallel to time axis. Statement 2: For the same particle x-t graph is a parabola.

7.

A particle is projected vertically upwards from a point A on the ground. It takes time t1 to reach a point B, but it still continues to move up. If it takes further t2 time to reach the ground from point B. Then height of point B from the ground is: 1 1 1 2 2 g t1 t2 g t1 t2 gt1t2 (A) (B) g t 1 t2 (C) (D) 2 8 2

VMC/Kinematics of a Particle

66

HWT/Physics

Vidyamandir Classes 8.

Two particles are released from the same height at an interval of 1s. How long after the first particle begins to fall will the two particles be 10 m apart. (g = 10 m/s2) (A) 1.5 s (B) 2s (C) 1.25 s (D) 2.5 s

9.

Velocity versus displacement graph of a particle moving in a straight line is as shown in figure. The acceleration of the particle is : (A) constant (B) increases linearly with x (C) increases parabolically with x (D) None of these

10.

V

X

A bus starts from rest and moves with an acceleration of 1.0 m/s2. A boy who is 48 m behind the bus runs after it with a constant speed of 10 m/s. The boy can catch the bus: (A) Only once after 8.0 seconds from the start (B) Only once after 12 seconds after start (C) Twice after 8 seconds, after 12 seconds from the start (D) Never

VMC/Kinematics of a Particle

67

HWT/Physics

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DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : KNM [1]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

A train accelerating uniformly from rest attains a

(A) (B) (C) (D)

maximum speed of 40 ms 1 in 20 s. It travels at this speed for 20 s and is brought to rest with uniform retardation in further 40 s. What is the average velocity during this period.

2.

(A)

80 / 3 ms 1

(B)

25 ms 1

(C)

40 ms 1

(D)

30 ms 1

3.

The graph below represents motion of a car. The displacement of the car in 20 s is : (A) (B)

4.

5.

6.

Two balls are dropped to ground from different heights. One ball is dropped 2 s after the other but the first ball hits the ground in 5 s, then, the difference in their heights is : (A) 125 m (B) 45 m (C) 80 m (D) 170 m

7.

A body starts from rest, with uniform acceleration a. The acceleration of a body as function of time t is given by the equation a = pt where p is constant, then the displacement of the particle in the time interval t = 0 to t = t1 will be.

On displacement-time graphs, two straight lines make angle 60 and 30 with time axis. The ratio of the velocities represented by them is : (A) 1:2 x(m) (B) 1:3 A (C) 2:1 60 30 t(s) (D) 3:1 O B C

20 m

(C)

90 m

(D)

10 m

8.

v(ms 1)

60 m

8 12

16 20

9.

Two particles A and B get 4m closer each second while traveling in opposite direction. They get 0.4 m closer every second while traveling in same direction. The speeds of A and B are respectively.

2.2 ms 1 and 0.4 ms 1

(B)

2.2 ms 1 and 1.8 ms 1

(C)

4 ms 1 and 0.4 ms 1 (D)

10. None of the above

A car is moving on a road and rain is falling vertically. Select the correct answer :

VMC/Kinematics of a Particle

1 3 pt 2 1

(B)

1 2 pt1 3

(C)

1 2 pt1 4

(D)

1 3 pt 6 1

A train starts form station with an acceleration 1ms 2 has

doubled? (A) 8s (C) 12 s

t(s)

–10

(A)

(A)

a velocity of 100 ms 1 . In what time, the velocity will be

10 4

The rain will strike the hind screen only The rain will strike the front screen only The rain will strike both the screens The rain will not strike any of screens

54

(B) (D)

10 s 14 s

A particle moves 200 cm in the first 2 s and 220 cm in the next 4 s with uniform deceleration. The velocity of the particle at the end of 7s is : (A)

12 cms 1

(B)

11 cms 1

(C)

10 cms 1

(D)

5 cms 1

The acceleration of a particle increases linearly with time t as 6t. If the initial velocity of the particle is zero and the particle starts from the origin, then the distance traveled by the particle in time t will be : (A) t (B) t2 3 (C) t (D) t4

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : KNM [2]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

2.

3.

A car starts from station and moves along the horizontal road by a machine delivering constant power. The distance covered by the car in time t is proportional to : (A) t2 (B) t3/2 2/3 (C) t (D) t3

7.

The displacement of a particle undergoing rectilinear motion along the x-axis is given by x = (2t2 + 21t2 + 60t + 6). The acceleration of the particle when its velocity is zero is : (A)

36 ms 2

(B)

9 ms 2

(C)

9 ms 2

(D)

18ms 2

7 ms 1

(C)

6 ms 1

(D)

5 ms 1

A particle is moving on a straight line path with constant acceleration directed along the direction of instantaneous velocity. Which of the following statements are false about the motion of particle? (A) Particle may reverse the direction of motion

(C) (D) 8.

second and vt in ms . The acceleration of the particle when it is 2 m from the origin is : (A)

28 ms 2

(B)

22 ms 2

(C)

12 ms 2

(D)

10 ms 2

A particle moving along a straight line has a

9.

A particle is moving with constant initial velocity 4 ms 1 10.

till t = 1.5 s. Then it accelerates at 10 ms 2 till t = 3. The distance covered is : (Take g 10 ms 2 ) (B) (D)

36.25 m 23.45 m

A car travels equal distances in the same direction with velocities 60 kmh 1 , 20 kmh 1 and 10 km h 1 respectively. The average velocity of the car over the whole journey of motion is :

VMC/Kinematics of a Particle

2

1 n

(D)

2 1 n n2

The velocity-time relation of an electron starting from rest is given by v = kt where k 2 ms 1 . The distance traversed in first 3 s is : (A) 9m (B) 16 m (C) 27 m (D) 36 m

When its velocity is 1ms 1 , its acceleration (in ms 2 ) is : (A) 1 (B) 2 (C) 7 (D) 0.5

17.25 m 40 m

2 n

These two are connected by the relation v 49 y .

(A) (C)

Distance covered is not equal to magnitude of displacement the magnitude of average velocity is less than average speed All of the above

A body starts from rest and moves with a constant acceleration. The ratio of distance covered in the nth second to the distance covered in n second is : 2 1 1 1 (A) (B) 2 n n n2 n (C)

velocity v ms 1 , when it cleared a distance of y metre.

6.

(B)

A body starts from origin and moves along x-axis such 1

5.

8 ms 1

(B)

that at any instant velocity is vt 4t 3 2t where t is in

4.

(A)

55

Which of the following statements is correct? (A) When air resistance is negligible, the time of ascent is less than the time of descent (B) When air resistance is not negligible, time of ascent is less than the time of descent (C) When air resistance is not negligible, the time of ascent is greater than the time of descent (D) When air resistance is not negligible, the time of ascent is lesser than the time of descent

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : KNM [3]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

: TIME TAKEN

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

A 2 m wide truck is moving with a uniform speed v0 8 ms 1 along a straight horizontal road. A pedestrian starts to cross the road with a uniform speed v when the truck is 4 m away from him. The minimum value of v, so that he can cross the road safely is : (A)

2.

4.

(B)

4.6 ms 1

3.57 ms 1

(C)

1.414 ms 1

(D)

A bus moves over a straight level road with a constant acceleration a. A body in the bus drops a ball outside. The acceleration of the ball with respect to the bus and the earth are respectively. (A)

3.

2.62 ms 1

a and g

(B)

a g and g a

a 2 g 2 and g (D)

(C)

a 2 g 2 and a

Two cars move in the same direction along parallel roads. One of them is a 100 m long traveling with a velocity of 7.5 ms 1 . How long will it take for the first car to overtake the second car? (A) 24 s (B) 40 s (C) 60 s (D) 80 s A car is moving along a straight road with uniform acceleration. It passes through two points P and Q separated by a distance with velocities 30 kmh 1 and 40 kmh 1 respectively. The velocity of car midway between P and Q is : (A)

5.

33.3 kmh 1

(B)

1 kmh 1

25 2 kmh 1

(C)

(D)

35.35 kmh 1

A particle starts from the origin and moves along the X-axis such that the velocity at any instant is given by 4t 3 2t , where t is in second and velocity is in ms–1. What is the acceleration of the particle when it is 2 m from the origin? (A)

10 ms 2

(B)

12 ms 2

22 ms 2

(C)

(D)

28 ms 2

–1

6.

The driver of a car moving with a speed of 10 ms sees a red light ahead, applies brakes and stops after covering 10 m distance. If the same car were moving with a speed of 20 ms–1, the same driver would have stopped the car after covering 30 m distance. Within what distance the car can be stopped if traveling with a velocity of 15 ms–1? Assume the same reaction time and the same deceleration in each case. (A) 18.75 m (B) 20.75 m (C) 22.75 m (D) 25 m

7.

If the velocity of a car is increased by 20%, then the minimum distance in which it can be stopped increases by : (A) 44% (B) 55% (C) 66% (D) 88%

8.

If the velocity v of a particle moving along a straight line decreases linearly with its displacement s from 20 ms–1 to a value approaching zero at s = 30 m, then acceleration of the particle at s = 15 m is : 2 2 2 ms ms 2 (A) (B) 3 3 20 2 20 2 ms ms (C) (D) 3 3

9.

V

(in ms 1 ) s (in m)

30

For a particle moving in a straight line, the displacement of the particle at time t is given by S t 3 6t 2 3t 7 . What is the velocity of the particle when its acceleration is zero? (A)

10.

20

9 ms 1

(B)

12 ms 1

3 ms 1

(C)

The displacement x of a particle at the instant when its velocity v is given by v (A)

1.5 units, 4 units

VMC/Kinematics of a Particle

(B)

3 units, 4 units

(C)

(D)

3x 16 . Its acceleration and initial velocity are

16 units, 1.6 units (D)

56

42 ms 1

16 units, 3 units

HWT/Physics

Vidyamandir Classes DATE :

IITJEE :

TIME : 25 MINUTES

MARKS : 10

NAME :

TEST CODE : KNM [4]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

: TIME TAKEN

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

A particle is moving with uniform acceleration along a straight line. The average velocity of the particle from P to Q is 8 ms 1 and that from Q to S is 12 ms 1 . If QS = PQ, then the average velocity from P to S is : (A)

9.6 ms 1

(B)

12.87 ms 1

64 ms 1

(C)

(D)

O P Q S

327 ms 1

2.

A particle starts from rest and travels a distance s with uniform acceleration, then it travels a distance 2 s with uniform speed, finally it travels a distance 3 s with uniform retardation and comes to rest. If the complete motion of the particle in a straight line then the ratio of its average velocity to maximum velocity is : (A) 6/7 (B) 4/5 (C) 3/5 (D) 2/5

3.

A particle moving in a straight line with uniform acceleration is observed to be a distance a from a fixed point initially. It is at distance b, c, d from the same point after n, 2n, 3n second. The acceleration of the particle is : c 2b a cb a c 2b a cba (A) (B) (C) (D) n2 9n 2 4n 2 n2

4.

A particle moves in a straight line so that its displacement x metre at time t second is given by t time t second is : (A)

1 x

5.

(B)

t2 x

3

1 t2 x x3

(C)

(D)

v1v2 v1 v2

(B)

2v1v2 v1 v2

3v1v2 v1 v2

(C)

(D)

1 x2

zero

6 + 4t = 0.2t2

Two cars leave one after the other and travel with and acceleration of 0.4 ms 2 . Two minutes after the departure of the first car, the distance between them becomes 1.90 km. The time interval between their departures is : (A) 50 s (B) 60 s (C) 70 s (D)

8.

x3

A man runs at a speed of 4 ms 1 to overtake a standing bus. When he is 6 m behind the door at t = 0, the bus moves forward and continues with a constant acceleration of 1.2 ms 2 . The man reaches the door in time t. Then, (A) 4t = 6 + 0.6 t2 (B) 1.2t2 = 4t (C) 4t2 = 1.2 t (D)

7.

t2

Three particles start from the origin at the same time, one with a velocity v1 along x-axis, the second along the y-axis with a velocity v2 and the third along x = y line. The velocity of the third so that the three may always lie on the same line is : (A)

6.

3

x 2 1 . Its acceleration in ms–2 at

80 s

The engine of a train can impart a maximum acceleration of 1 ms 2 and the brakes can give a maximum retardation of 3 ms 2 . The least time during which a train can go from one place to the other place at a distance of 1.2 km is nearly. (A) 108 s (B) 191 s (C) 56.6 s (D) time is fixed

VMC/Kinematics of a Particle

57

HWT/Physics

Vidyamandir Classes 9.

The acceleration of a particle increasing linearly with time t is bt. The particle starts from the origin with an initial velocity v0. The distance traveled by the particle in time t will be : 1 1 1 1 v0t bt 3 v0t bt 2 v0t bt 3 v0t bt 2 (A) (B) (C) (D) 6 3 3 3

10.

In the given v-t graph, the distance travelled by the body in 5s will be : (A) 20 m (B) 40 m (C) 80 m (D) 100 m

VMC/Kinematics of a Particle

58

40 30 20 V (in ms 1 ) 10 0 –10 –20

2

3

4

5

time (in sec)

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : KNM [5]

ROLL NO.

START TIME :

END TIME :

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PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking.

2.

3.

Figure gives the speed - time of the motion of a car. What is the ratio of the distance traveled by the car during the last two seconds to the total distance traveled in seven seconds ? (A) 1/9 (B) 2/9 (C) 1/3 (D) 4/9

12 ms 1

14ms 1

(C)

10 5

16ms 1

(D)

m1u m2

(B)

m2u m1

m1 m2 m1 m2

(C)

The displacement y (in meters) of a body varies with time t (in seconds) as y

(C)

(D)

u

2 2 t 16t 2 3

12 seconds

(D)

16 seconds 30

The velocity – time graph of a stone thrown vertically upward with an initial velocity of 30ms 1 is shown in the figure. The velocity in the upward direction is taken as positive and that in the downward direction as negative. What is the maximum height to which the stone rises? (A) 30 m (B) 45 m (C) 60 m (D) 90 m

7.

15

Two balls of mass m1 and m2 are thrown vertically upward with the same speed u. If air resistance is neglected, they will pass through their point of projection in the downward direction with a speed :

How long does the body take to come to rest? (A) 8 seconds (B) 10 seconds 6.

B

The acceleration of (in ms 2 ) of a body, starting from rest varies with time t (in s) according to the relation a 3t 4 . The velocity of

(A) 5.

A

E C D 1 2 3 4 5 6 7 Time (s) A stone falls from rest. The distance covered by the stone in the last second of its motion equals the distance covered by it during the first three seconds of its motion. How long does the stone take the reach the ground ? (A) 4s (B) 5s (C) 6s (D) 9s

the body at time t = 2s will be: (A) (B) 10ms 1 4.

25 20

Velocity (ms–1)

1.

Speed (ms–1)

Choose the correct alternative. Only one choice is correct.

A

20 10 B 10

1 2

3

Time (s) 4 5

6

20 30

C

1

At t = 0, an arrow is fired vertically up-wards with a speed of 98ms . A second arrow is fired vertically upwards with the same speed at t = 5s. Then: (A) the two arrows will be a the same height above the ground at t = 10s (B) the two arrows with reach back their staring point at t = 20 s and at t = 30s (C) the ratio of the speeds of the first and the second arrows at t = 20s will be 2 : 1 (D) the maximum height attained by either arrow will be 980 m

VMC/Kinematics of a Particle

59

HWT/Physics

Vidyamandir Classes 8.

The area under the velocity – time graph between any two instant t t1 and t t2 gives the distance covered in time t t2 t1 (A) Only if the particle moves with a uniform velocity (B) only if the particle moves with a uniform acceleration (C) Only if the particle moves with an acceleration increasing at a uniform rate (D) In all case irrespective of whether the motion in one of uniform velocity, or of uniform acceleration or of variable acceleration.

9.

Which of the following statement is wrong? (A) If speed of a particle changes, its velocity must change. (B) If velocity of a particle doesn’t change, its speed must remain constant (C) If speed of a particle doesn’t change, its velocity must remain constant (D) If velocity of a particle changes, its speed may or may not change

10.

The variation in the speed of a car during its two hour journey is shown in the graph of Figure. The magnitude of the maximum acceleration of the car occurs during the interval. (A) OA (B) BC (C) CD (D) DE

VMC/Kinematics of a Particle

60

100 80 60 40 20

E C D

A B 0.5

1.0 1.5 2.0

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : KNM [6]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

: TIME TAKEN

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct 1.

A parachutist drops freely from an aeroplane for 10s before the parachute opens out. Then he descends with an net retardation of 2.5ms 2 . If he bails out of the plane at a height of 2495 m and g = 10ms 2 , his velocity on reaching the ground will be : (A)

2.

(B)

7.5 ms 1

5 ms 1

(C)

(D)

10ms 1

A car accelerates from rest at a constant rate for some time after which it decelerates at a constant rate to come to rest. If the total time elapsed is t, the maximum velocity acquired by the car is given: (A)

3.

2.5 ms 1

t

(B)

t

(C)

2 2 t

(C)

1 2 2 2 t (D) 2

(D)

2 t

The distance traveled by the car in Q 2 above is given by : (A)

1 2 t 2

(B)

1 2

2 t

1 1 2 2 t 2

4.

Water drops fall at regular intervals from a roof. At an instant when a drop is about to leave the roof, the separations between 3 successive drops below the roof are in the ratio: (A) 1:2:3 (B) 1:4:9 (C) 1:3:5 (D) 1 : 5 : 13

5.

A freely falling body, falling from a tower of height h covers a distance h/2 in the last second of its motion. The height of the tower is (Take g = ms–2) nearly (A) 58 m (B) 50 m (C) 60 m (D) 55 m

6.

Ball A is rolled in a straight line with a speed of 5ms–1 towards a bigger ball B lying 20 m away. After collision with ball B, ball A retraces the path and reaches its starting point with a speed of 4ms 1 . What is the average velocity of ball A during the time interval 0 to 6s? (A) zero (B) 2 ms–1 (C) 4 ms–1 (D) 5 ms–1

7.

A train moving southwards at a speed of 30ms 1 . A monkey is running northwards on the roof of the train with a speed of 5ms 1 . What is the velocity of the monkey as observed by a person standing on the ground? (A)

35ms 1 in the southward direction

(B)

(C)

25ms 1 in the southward direction

(D)

35ms 1 in the northward direction 25ms 1 in the northward direction –1

8.

A jet airplane traveling from east to west at a speed of 500 kmh ejects out gases of combustion at a speed of 1500 kmh–1 with respect to the jet plane. What is the velocity of the gases with respect to an observer on the ground? (A) 1000 kmh–1 in the direction west to east (B) 1000 kmh–1 in the direction east to west –1 (C) 2000 kmh in the direction west to east (D) 2000 kmh–1 in the direction east to west

9.

A police van moving on a highway with a speed of 36 kmh–1 fires a bullet at a thief’s car speeding away in the same direction with a speed of 108kmh 1 . If the muzzle speed of the bullet is 140 ms–1, with what speed will the bullet hit the thief’s car? (A) 120 ms–1 (B) 130 ms–1 (C) 140 ms–1 (D) 150 ms–1

10.

Two persons P and Q are standing 54 m apart on a long moving belt. Person P rolls a round stone towards person Q with a speed of 9 ms–1 with respect to the belt. If the belt is moving with a speed of 4 ms–1 in the direction from P to Q, what is the speed of the stone with respect to an observer on a stationary platform? (A) 4 ms–1 (B) 5 ms–1 (C) 9 ms–1 (D) 13 ms–1

VMC/Kinematics of a Particle

61

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : KNM [7]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

: TIME TAKEN

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

2. 3.

From the top of a multi-storied building 40 m tall, a body projects a stone vertically upwards with an initial velocity 10ms 1 such that it eventually falls to the ground. After how long will the stone strike the ground? Take g = 10ms 2 (A) 1s (B) 2s (C) 3s (D)

4s

In Q.1 above, after how long will the stone pass through the point from where it was projected ? (A) 1s (B) 2s (C) 3s (D)

4s

In Q.1, what will be the speed of the stone when it strikes the ground ? (A)

4.

10ms 1

(B)

20ms 1

30ms 1

(C)

(D)

40 ms 1

A balloon is rising vertically upwards at a velocity of 10ms 1 . When it is at a height of 45m from the ground, a parachutist bails out from it. After 3 s he opens his parachute and decelerates at a constant rate of 5ms 2 . What was the height of the parachutist above the ground when he opened his portraiture? Take g = 10ms 2 (A) 15 m (B) 30 m (C)

45 m

(D)

60 m

5.

Two identical balls are shot upward one after another at an interval of 2 s along the same vertical line with same initial velocity of 40 m/s. The balls collide after ns the first ball is shot. What is the value of n? (A) 2 (B) 3 (C) 4 (D) 5

6.

Water in a well is at a depth h. A ball is released from ground so that it falls, into the well. The speed of sound in air is c. The time after which sound of splash is heard is : (A)

7.

2h h g 2c

(C)

(D)

h h g c

3kmh 1

(B)

6kmh 1

9khm 1

(C)

(D)

r O

60

r

12kmh 1

3 cot 1 with the vertical towards south 4

3 cot 1 with the vertical towards north 4

(D)

A swimmer can swim in still water with a speed of 3ms 1 .While crossing a river his average speed is 5ms 1 . If he crosses the river in the shortest possible time, what is the speed of flow of water? (A)

10.

2h h g c

Rain is falling vertically with a speed of 4ms 1 . After some time wind starts blowing with a speed of 3ms 1 in the north to south direction. In order to protect himself from rain, a man standing on the ground should hold his umbrella at an angle given by: 3 3 (A) tan 1 with the vertical towards south (B) tan 1 with the vertical towards north 4 4 (C)

9.

(B)

A cyclist starts from the centre O of a circular track of radius r = 1 km, reaches the edge P of the track and then cycles along the circumference and stops at point Q as shown in Figure. If the total time taken is 10 min, what is the average velocity of the cyclist? (A)

8.

2h 2h g c

2ms 1

(B)

4ms 1

5ms 1

(C)

(D)

6ms 1

A body starting from rest, moves in a straight line with a constant acceleration a for a time interval t during which it travels a distance s1. If continues to move with the same acceleration for the next time interval t during which it travels a distance s2. The relation between s1 and s2 is : (A) (B) (C) (D) s2 s1 s2 2 s1 s2 3s1 s2 4 s1

VMC/Kinematics of a Particle

62

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : KNM [8]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

: TIME TAKEN

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

A body dropped from the top of a tower hits the ground after 4 s. How much time does it take to cover the first half of the distance from the top of the tower? (A)

2.

3.

4.

(B)

2s

(C)

(D)

2 2s

3s

A body moving in a straight line with constant acceleration of 10ms 2 covers a distance of 40 m in the 4th second. How much distance will it cover in the 6th second? (A) 50 m (B) 60 m (C) 70 m (D) 80 m A body, moving in a straight line with an initial velocity of 5ms 1 and a constant acceleration, covers a distance of 30 m in the 3rd second. How much distance will it cover in the next 2 seconds? (A) 70 m (B) 80 m (C) 90 m (D) 100 m A body, moving in a straight line, with an initial velocity u and a constant acceleration a, covers a distance of 40 m in the 4th second and a distance of 60 m in the 6th second. The value of u and a respectively are: (A)

5.

1s

10ms 1,5ms 2

(B)

10ms 1 10ms 2

5ms 1 5ms 2

(C)

(D)

5ms 110ms 2

A body, starting from rest and moving with a constant acceleration, covers a distance s1 in the 4th second and a distance s2 in the 6th second. The ratio s1 / s2 is: (A)

2/3

(B)

4/9

(C)

6/11

(D)

7/11

6.

A car, starting from rest, has a constant acceleration a1 for a time interval t1 during which it covers a distance s1. In the next time interval t2 the car has a constant retardation a2 and comes to rest after covering a distance s2 in time t2. Which of the following relations is correct? a1 s2 t2 a1 s t a1 s2 t1 a1 s t (A) 1 1 (B) (C) 1 2 (D) a2 s1 t1 a2 s2 t2 a2 s1 t2 a2 s2 t1

7.

In Q.6 if the total distance covered by the car is s, the maximum speed attained by it will be : 1

(A)

a1a2 2 2s . a 1 a2

1

(B)

a1a2 2 2s . a 1 a2

1

s a1a2 2 . 2 a 1 a2

(C)

1

(D)

s a1a2 2 . 2 a 1 a2

8.

A car, starting from rest, is accelerated at a constant rate until it attains a speed v. It is then retarded at a constant rate until it comes to rest. The average speed of the car during its entire journey is: v v v (A) zero (B) (C) (D) 2 2 2

9.

The displacement of a body from a reference point, is given by : Where x is in metres and t in seconds. This shows the body is: (A) at rest (B) accelerated (C)

10.

x 2t 3

decelerated

(D)

in uniform motion

6ms 1

(D)

12ms 1

In Q.9, what is the initial velocity of the body? (A)

2ms 1

VMC/Kinematics of a Particle

(B)

3ms 1

(C)

63

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : KNM [9]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

: TIME TAKEN

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

2.

A car is moving at a certain speed. The minimum distance over which it can be stopped is x. If the speed of the car is doubled, what will be the minimum distance over which the car can be stopped ? (A) 4x (B) 2x (C) x/2 (D) x/4 A bullet is fired vertically upwards with an initial velocity of 50ms 1 . It covers a distance h1 during the first second and a distance h2 during the last 3 seconds of its upward motion. If g 10ms 2 , h1 and h2 will be related as :

3.

4.

h h1 2 3 A ball is thrown vertically downward with a velocity u from the top of a tower. It strikes the ground with a velocity 3u. the time taken by the ball to reach the ground is given by:

(A)

h1 3h2

(B)

h1 2h2

(C)

h1 h2

(D)

(A)

u g

(B)

2u g

(C)

3u g

(D)

4u 2 g

In Q.3, the height of the tower is given by :

5.

u2 2u 3u 4u 2 (B) (C) (D) g g g g A ball is dropped from the top of a building 3.2 m high and it rebounds to a height of 1.8 m. The ball is in contact with the floor for 0.05 s. What is ball’s average acceleration during this period? (Use g = 10 m/s2) (A) 180 m/s2 (B) 280 m/s2 (C) 380 m/s2 (D) 480 m/s2

6.

The distance x covered by a body moving in a straight line in time t is given by the relation

(A)

2 x 2 3x t If v is the velocity of the body at a certain instant of time, its acceleration will be:

v3

(A) 7.

2v3

3v3

(C)

4v3

(D)

The v-x graph for a particle moving along a straight line is shown in the figure. At which of the points marked, the object is slowing down? (A) 1 (B) 3 (C) 1 and 2 (D)

8.

(B)

v 2 3

1

x

t(s)

3 and 2

The body starts from rest at time t = 0 and undergoes an acceleration as shown in Figure. Which of the graphs shown in figure represents the velocity - time (v – t) graph of the motion of the body from t = 0 s to t = 4s) 6 v 3 (ms–1) 0

A C

v 3 (ms–1)

B 1 2 3 t(s) (A)

6

4

VMC/Kinematics of a Particle

0

A

B

D 1 2 3 t(s) (B)

B

6 v 3 (ms–1)

C

0

4

64

6

A 1 2 3 t(s) (C)

C 4

v 3 (ms–1) A 0

B C

D 1 2 3 t(s) (D)

4

HWT/Physics

Vidyamandir Classes 9.

A body, moving in a straight line, covers half the distance with a speed V, the remaining part of the distance was covered with a speed V for half the time and with a speed V for the other half of the time. What is the average speed of the body? (A)

10.

2V V V

2V

V V

(B)

V V V

2V

V V

2V V V V V

(C)

(D)

V V V V V

A car is moving on a straight horizontal road with a speed v. When brakes are applied to give a constant retarding a, the are is stopped in a shortest distance S. If the car wares moving on the same road with a speed 3 v and the same retardation a is applied, the shortest distance in which the car is stopped will be: (A) 3S (B) 6S (C) 9S (D) 27 S

VMC/Kinematics of a Particle

65

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : KNM [10]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

: TIME TAKEN

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

A particle starts from rest at t = 0 and moves in a straight line with an acceleration as shown below. The velocity of the particle at t = 3s is : (A) (B) (C) (D)

2.

2 m/s 3 m/s 4 m/s 6 m/s

4.

3 t(s)

0 1 2

–3

mv 2 2t

v2 2T

(B)

(C)

4

3

v

The velocity-time graph of a body is shown in figure. The slope of the line is ‘m’. The distance travels by body in time Ts (A)

3.

a(m/s)

v

2mv2

(D)

The graph describes an airplane’s acceleration during its take-off run. The airplane’s velocity when it lifts off at t = 20s is: (A) 40 m/s (B) 50 m/s (C) 90 m/s (D) 180 m/s

v2 2m

a(m/s2)

O

t

T

5 3 O

10

20 t(s)

A parachutist jumps out of an aircraft, falls freely for some time and then opens his parachute. Identify the graph which correctly represents his acceleration (a) versus time (t) graph: a a a a

(A)

0

t

(B)

0

t

(C)

0

t

(D)

0

t

For Q.5 - 6 (A) (B) (C) (D)

Statement-1 is True, Statement-2 is True and Statement-2 is a correct explanation for Statement-1 Statement-1 is True, Statement-2 is True and Statement-2 is NOT correct explanation for Statement-1 Statement-1 is True, Statement-2 is False Statement-1 is False, Statement-2 is True

5.

A ball is thrown vertically upwards from ground. At its highest point. Statement 1: Velocity = 0. Statement 2: Acceleration = 0.

6.

A particle is in uniform motion. Statement 1: For the particle v-t graph is a straight line parallel to time axis. Statement 2: For the same particle x-t graph is a parabola.

7.

A particle is projected vertically upwards from a point A on the ground. It takes time t1 to reach a point B, but it still continues to move up. If it takes further t2 time to reach the ground from point B. Then height of point B from the ground is: 1 1 1 2 2 g t1 t2 g t1 t2 gt1t2 (A) (B) g t 1 t2 (C) (D) 2 8 2

VMC/Kinematics of a Particle

66

HWT/Physics

Vidyamandir Classes 8.

Two particles are released from the same height at an interval of 1s. How long after the first particle begins to fall will the two particles be 10 m apart. (g = 10 m/s2) (A) 1.5 s (B) 2s (C) 1.25 s (D) 2.5 s

9.

Velocity versus displacement graph of a particle moving in a straight line is as shown in figure. The acceleration of the particle is : (A) constant (B) increases linearly with x (C) increases parabolically with x (D) None of these

10.

V

X

A bus starts from rest and moves with an acceleration of 1.0 m/s2. A boy who is 48 m behind the bus runs after it with a constant speed of 10 m/s. The boy can catch the bus: (A) Only once after 8.0 seconds from the start (B) Only once after 12 seconds after start (C) Twice after 8 seconds, after 12 seconds from the start (D) Never

VMC/Kinematics of a Particle

67

HWT/Physics

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