Problem Set 2 Dynamics

1

PROBLEM SET 2

Part 1 VARIABLE ACCELERATION 1. The rectilinear motion of a particle is given by S=V2-9 where S is in meter and V is meter per second. When t=0, S=0 and V=3m/s. Determine (a) relation between S and t, (b) relation between V and t, (c) relation between a and t. 2. A car is travelling at the speed V0 on a straight level road. After the brakes are applied at 𝑡2

t=0, the motion can be approximated by 𝑥 = 100 − 𝑡 2 + 17𝑡 where x is the distance traveled in meters and t is the time in seconds. Determine (a) value of V0 (b) distance required for the car to stop (c) maximum acceleration during braking. 3. A curvilinear motion of a particle is defined by Vx=40-15t and y=75-3t2 where Vx is in meter per second. It is also known that x=0 when t=0. Determine (a) the second value of time “t” when “x” will be equal to zero, (b) velocity when x=0 at the second value of time, (c) acceleration when X=0 at the second value of time. 4. The rocket starts from rest t=0 and travels straight up. Its height above the ground can be approximated by the function S=bt2+ct4 where “b” and “c” are constants. At t=10sec the rockets velocity and acceleration are V=229 m/s and a=28.2 m/s2. Determine (a) “S” at t=5sec (b) velocity at t=5sec (c) acceleration at t=5sec. 5. The acceleration of a point is a=20t m/s2. When t=0, S=40m and V=-10m/s. Determine (a) position of the point at t=3sec (b) velocity of the point at t=3sec (c) acceleration of the point at t=3sec. 6. A race car starts from rest and accelerates at a=5+2t m/s2 for 10 sec. The brakes are then applied and the car has constant acceleration of a=-30m/s2 until it comes to rest. Determine (a) maximum velocity (b) total distance traveled (c) total time of travel. 7. The acceleration of a point moving along a straight line a=4t+2 (m/s2). When t=2sec, the position of the point is S=36m and when t=4sec, its position S=90m. Determine (a) acceleration of the point when t=4sec (b) velocity of the point when t=4sec (c) position of the point when t=3sec. 8. The velocity of a particle which moves along the S-axis is given by V=2-4t+5t3/2 where t is in seconds and V in meters per second. The particle is at the position So=3m when t=0. Determine (a) position S when t=3sec. (b) velocity of the particle when t=3sec. (c) acceleration of the particle when t=3sec. 9. The motion of a particle is governed by the relation a=4t2 where a is in m/s2 and t is in seconds. When t is zero, V=2m/s and S=4m. Determine (a) velocity when t=2sec (b) distance when t=2sec (c) acceleration when t=2sec. 10. The velocity of a particle moving along the x axis is defined by V=x3-4x3+6x where V is in m/s and x is in m. Determine (a) velocity when x=2m (b) acceleration when x=2m.

DYNAMICSmks1516

2

Part 2 MOTION CURVES 11. A train is brought to an emergency stop in 16 seconds, the deceleration being shown in the diagram. Determine (a) the time when the deceleration becomes zero (b) speed of the train before the brakes were applied (c) stopping distance.

12. A car starting from rest accelerates uniformly from zero to V to 3m/s 2 for 5sec at C then decelerates uniformly at 2m/s2 and stop at D. Compute the time the car has traveled from B to D. 13. A train upon passing point A at a speed of 72 kph accelerates at 0.75 m/s2 for one minute along a straight path then decelerates at 1.0m/s2. How far in km from point A will it be 2 min after passing point A. 14. A car accelerates uniformly from zero to 12m/sec2 in 8 seconds starting from rest. During the next 4seconds, the car decelerates uniformly at a constant rate of 11m/s2. Determine (a) velocity of the car after 12 seconds (b) distance traveled after 10 seconds (c) total distance traveled after 12 seconds. 15. A car accelerates from initial velocity of 10m/s. The acceleration is increasing uniformly from zero to 8m/s2 in seconds. During the next two seconds, the car decelerates at a constant rate of 2 m/s2. Determine (a) velocity after 8 seconds (b) distance traveled after 6 seconds (c) total distance traveled after 8 seconds.

DYNAMICSmks1516