1 A particle starts from rest and accelerates uniformly for 5 s until it reaches a speed of 10 m/s. It immediately decelerates uniformly until it comes to rest after a further 8 s. How far did it travel?
2 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.
3 A particle starts from rest and travels 1 km before coming to rest again. For the first 5 s it accelerates uniformly. It next maintains a constant speed for 500 m, and then decelerates uniformly for the last 10 s. And the maximum speed of the particle.
4 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?
5 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.
6 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?
7 A particle is moving in a straight line. The initial velocity of the particle is 20 m/s and it has a constant acceleration of —2 m/s2. a Sketch the velocity—time graph for the motion. b Describe the motion of the particle during the first 14 seconds. c Find the total distance travelled in the first 14 seconds of motion. d Find the displacement of the particle after the first 14 seconds of motion.
8 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 r = 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.
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9 A particle moves in a straight line, starting from rest at a point 0. 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.
10 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 pacces 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?
11 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/s2, before coming to rest at the second stop. The time taken to travel between the two stops is I 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.