Motion Along a Straight Line

MOTION ALONG A STRAIGHT LINES (FORM 5)

1.

A particle moves along a straight line through a fixed point O. Its displacement, displacement, s metres 2 from O is given by  s = −t  + 7t  − 10 where t is the time, in second, after leaving O. Assume motion to the right is positive. Find (a) the maximum displacement (b) the range of time when the particle is moving to right. (c) the distance of the particle from O when its velocity is -5 ms −1

2.

Diagram shows two fixed point, A and B, on a horizontal straight line. A particle P starts from A and moves along the straight line. It velocity, v ms-1, is given by v = 15 − 3t  , where t  is the time in seconds after passing through the point A. Initially, motion P is t owards B.

(a) Find the range of values of  t  during which the particle is moving toward B marks] (b) If the distance of AB is 37m, determine whether the particle reaches B in its motion. (c) Find the total distance traveled by the particle in the first 8 seconds (d) Sketch the graph of  S  against t  for the range 0 ≤ t  ≤ 8 S  represents the displacement displacement of the particle from the fixed point A

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5

The displacement of a particle Q that moves in a straight line from a fixed point 0, is given by  s = t 3 − 6t 2 + 9t  . Find (a) the initial velocity of particle Q, (h) the values of t when the particle Q change its direction of the motion, (c) the acceleration acceleration of particle Q after 4 seconds. (d) the maximum velocity of particle Q.

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[3 marks] [3 marks] [2 marks]

[2 marks] [2 marks] [3 marks] [3 marks]

A particle moves along along a straight line line from a fixed point point O. Its displacement displacement , s m from O is 3 2 given by  s = −t  + 2t  + 3t  , where t is the t he time, in second, after leaving O. Find (a) the velocity of the particle when its passes through O again. [3 marks] (b) the maximum velocity of the particle [4 marks] 1 − (c) the acceleration of the particle when its velocity is -1 ms [3 marks]

A particle moves along a straight straight line from a fixed fixed point O. Its velocity, v m/s, is given by v 3t (5 t ) , where t  is the time, in seconds, after leaving point O. Find (a) the maximum velocity of the particle (b) the distance traveled in the third second (c) the displacement displacement when the particle particle is at instantaneous instantaneous rest (d) the value of  t  when the particle passes through point O again. =

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Prepared by: NORHASHIMAH BT. ABDUL MAJID

6

A particle moves along a straight through a fixed point O. its acceleration, a m s-2, is given by a = 3t  − 9 , where t is the time, in seconds, after passing point O. find (a) the maximum velocity of the particle (b) the time when the particle is at instantaneous rest (c) the displacement when the particle is at instantaneous rest (d) the velocity at which the particle returns to O

7

A particle moves along a straight line from a fixed point O. its velocity, v m s-1, is given by v 2t (6 t ) , where t is the time, in seconds, after leaving point O. find. (a) The time when the particle is at instantaneous rest (b) The distance traveled when 1 ≤ t  ≤ 3 (c) The value of t when the particle passes through point O again (d) The velocity at which the particle returns to O =

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8.

6. A particle moves along a straight line so that its acceleration, a m/s2, is given by a = 2t  − 8 , where t  is the time, in second, after passing through the fixed point O. The initial velocity of the particle is 12 ms −1 . Find (a) the velocity of the particle when its acceleration is zero. (b) the time at which the particle is instantaneously at rest (c) the total distance traveled by the particle in the f irst three second.

9.

.A particle P traveling in a straight line passes a fixed point O with a velocity of  4ms 1 . Its acceleration a ms 2 , is given by the equation a = 4 − 2t  where t is the time , in second after  passing O. (a) Show that the velocity, v ms −1 , is given by v = 4t  − t 2 − 4 (b) find the instant when P is instantaneously at rest. (c) Find the displacement of P when its velocity is 4ms 1 −

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10.

The displacement,  s m, of a particle moving in a straight line from a fixed point O is given by 2  s = t  − 2t  − 3 , where t  is the time in seconds after passing O. (a) Find the initial velocity (b) Find the time when the particle is at instantaneous rest (c) Sketch the velocity – time graph for  0 ≤ t  ≤ 4 (d) Hence, find the total distance traveled in the first 4 seconds.

11.

The velocity, v ms-1, of a particle moving in a straight line is given by v = 6t  − kt 2 , where k  is a constant and t  is the time in seconds after passing a fixed point O. The acceleration is zero when t  1 (a) Find the value of k (b) Find the maximum velocity of the particle (c) Find the time when the particle comes to instantaneous rest (d) Sketch the velocity-time graph for  0 ≤ t  ≤ 3 (e) Hence, find the total distance traveled in the first 3 seconds. =

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Prepared by: NORHASHIMAH BT. ABDUL MAJID

12

A particle moves along a straight line so that its displacement, time t  seconds is given by  s = 2t 3 − 15t  + 24t  + 20 . Find (a) the initial velocity (b) the time when it is momentarily at rest (c) the minimum distance of the particle from the point O. (d) the range of time when the body is moving towards O (e) the maximum velocity

13

A particle moves in a straight line and passes through a fixed point O with the velocity of 12 2 −1 , Its acceleration a is given by a = 4 − 2t  where t is the time, in seconds. After  ms 12 ms it passes O, the particle stop instantaneously at the point A. Find. (a) the time taken by the object to reach point A from point O. [4 marks] (b) the distance of OA [2 marks] (c) the maximum velocity of the object [2 marks] (d) the whole distance which the object has passed on in the first 7 seconds [3 marks]

 s

m, from a fixed point O at

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14  A  P 

Diagram shows the particle A moves in a straight line and passes through a fixed point P. Its velocity, vms 1 , is given by v = 15t  − 3t  2 where t is the time, in seconds, after leaving O. [Assume motion to the right is positive] Find (a) the maximum velocity, in m s -1. of  A [3 marks] (b) the time when the particle is at O again. [4 marks] (c) the range of time when the velocity of the particle is negative. [3 marks] −

15

Two particles A and B are travelling in the same direction along a straight line. The velocity of particle A, V  A ms-1, is given by V  A = 10 - 10t and the velocity of particle B, V B ms1 , is given by V B = 3t 2 - 8t + 4 where t is the time, in seconds, after passing point O. Find (a) the acceleration of particle B at the moment of passing point O, [2 marks] (b) the time interval when particles A and B move in the same direction again, [2 marks] (c) the distance travelled by particle A during the interval of two seconds after it has momentarily stop, [3 marks] (d) the time when particle A will meet with particle B again. [3 marks]

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Prepared by: NORHASHIMAH BT. ABDUL MAJID