A motorist traveling at a constant velocity of 17 m/s passes a school-crossing c

Question

A motorist traveling at a constant velocity of 17 m/s passes a school-crossing corner where the speed limit is 12 m/s. A police officer on a motorcycle originally stopped at the corner starts off in pursuit with constant acceleration of 3.2 m/s^2.

1. How much time elapses before the officer catches up with the car?

2. What is the distance the officer has traveled at that point?

3. What is the officer's speed at that point?

4. The officer asked the driver to stop the car. The driver starts to slow down the car at constant acceleration and the car stopped after traveling 60 m from the point where the officer caught up with the car. What was the acceleration of the car before it stopped?

* If you answer the questions, please explain how you reasoned that out!

Thank you!!!

Explanation / Answer

The constant velocity of the motorist is vm = 17 m/s

The acceleration of the police is ap = 3.2 m/s

As the police caught the motorist, both will travell same distance from the point wher police started

a)

Let t be the time elapses before the officer catches up with the car

The distance travelled by the motorist dm = vmt

dm = 17t

THe distance travelled by the police dp = 0.5*ap*t2             (u = 0)

dp = 0.5*3.2t2

dp = 1.6t2

As dm = dp

17t = 1.6t2

Either t = 0 or t = 10.625 s

Therefore the time elapses before the officer catches up with the car is 10.625 s

b)

THe distance travelled by the police dp = 0.5*ap*t2             (u = 0)

dp = 0.5*3.2*10.6252

dp = 180.625 m

c)

The speed of the police at that point will be

vp = ap*t               (u=0)

vp = 3.2*10.625

vp = 34 m/s

d)

As the car stopped after traveling D = 60 m from the point where the officer caught up with the car

Let a be the acceleration of the car

then

02 - vm2 = 2aD

- 172 = 2*a*60

a = - 2.408 m/s2  

negative sign indicates that the car is slowing down

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