# 3. Kinematics Exercises

1. A charged particle in an accelerator starts from rest, accelerates at 1.5\ "ms"^-2 for 3\ "s" and then continues at a steady speed for a further 6\ "s".

Draw the v-t graph and find the total distance travelled.

2. A speedboat starts from rest, accelerating at 2\ "ms"^-2 for 20\ "s". It then continues at a steady speed for a further 30\ "s" and decelerates to rest in 30\ "s". Find:

(a) the distance travelled in "m",

(b) the average speed in "ms"^-1 and,

(c) the time taken to cover half the distance.

3. A car is travelling at a constant speed of 72\ "km/h" and passes a stationary police car. The police car immediately gives chase, accelerating uniformly to reach a speed of 90\ "km/h" in 10\ "s" and continues at this speed until he overtakes the other car. Find:

(a) the time taken by the police to catch up with the car,

(b) the distance travelled by the police car when this happens.

4. Two sport cars start from rest at the same place. One of them, colored red, accelerates at 0.90\ "ms"^-2 for 15\ "s", and continues at constant speed thereafter. The other car, colored blue, accelerates at 0.85\ "ms"^-2 for 20\ "s" and then remains at that speed.

Draw both journeys on the same velocity-time graph and determine the time and distance that the second car overtakes the first car.

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