# 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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