1) A car accelerates uniformly from rest for 10 s to a speed of 15 m/s. It maintains this speed for 25 s before decelerating uniformly to rest after a further 15 s. Find: a) the total distance...

1) A car accelerates uniformly from rest for 10 s to a speed of 15 m/s. It maintains this speed for 25 s before decelerating uniformly to rest after a further 15 s. Find: a) the total distance travelled by the car b) the distance it had travelled when it started to decelerate c) the time taken for it to reach the halfway point of its journey 2) A car passes point P with a speed of 36 km/h and continues at this speed for 12 s before accelerating to a speed of 72 km/h in 6 s. How far from P is the car when it reaches a speed of 72 km/h? 3) A tram decelerates uniformly from a speed of 60 km/h to rest in 60 s. Find: a) the distance travelled by the tram b) how far it had travelled by the time it had reduced its speed by half c) the time taken for it to travel half the total distance. 4) A car passes a point A with a speed of 15 m/s and continues travelling at that speed. A second car is stationary at point A. At the moment when the first car passes A, the second car accelerates uniformly until it reaches a speed of 25 m/s in 10 s. Both cars continue with a constant speed on to point B, which they reach at the same time. a) How long does it take for both cars to reach point B? b) How far is it from A to B? 5) The velocity–time graph for the motion of a particle is shown. a) Find the acceleration for the first 10 seconds. b) Find the acceleration for the period from t = 20 to t = 30, where t is the time in seconds from the beginning of the motion. c) Find the total distance travelled in the first 30 seconds. d) Find the displacement of the particle after 30 seconds Specialist math - Kinematics 6) A particle moves in a straight line, starting from rest at a point O. It first moves in a positive direction with an acceleration of 2 m/s2 , until its velocity reaches 10 m/s. It then continues with a constant velocity of 10 m/s for some time, before decelerating to rest after a total time of 20 seconds. The total distance travelled is 160 m. a) Sketch the velocity–time graph. b) Find the magnitude of the deceleration. 7) Two stations A and B are 14 km apart. A train passes through station A, heading towards B, maintaining a constant speed of 60 km/h. At the instant that it passes through A, a second train on the same track leaves station B, heading towards A, and accelerates uniformly. After 5 minutes, the alarm is raised at both stations simultaneously that a collision is imminent. Both trains are radioed and instructed to brake. The first train decelerates uniformly so that it will stop in 2.5 minutes. The second train, which has reached a speed of 80 km/h, will take 4 minutes to stop. Will they collide? 8) Two tram stops are 800 m apart. A tram starts from rest at the first stop and accelerates at a constant rate of a m/s2 for a certain time and then decelerates at a constant rate of 2a m/s 2 , before coming to rest at the second stop. The time taken to travel between the two stops is 1 minute 40 seconds. Find: a) the maximum speed reached by the tram (in km/h) b) the time at which the brakes are applied c) the value of a