A motorist drives along a straight road at a constant speed of 16.5 m/s....?

Question

A motorist drives along a straight road at a constant speed of 16.5 m/s. Just as she passes a parked motorcycle police officer, the officer starts to accelerate at 1.00 m/s2 to overtake her. Assume that the officer maintains this acceleration.

Determine the time it takes the police officer to reach the motorist.

Find the speed of the officer as he overtakes the motorist.

Find the total displacement of the officer as he overtakes the motorist.

Answer 1

In this problem, you must remember that the motorist and police officer are both moving.
Let's reprase the question - at what time will the two drivers have the same displacement?

This one is obvious:
Distance = 16.5 * time

Now we apply s = ut + 1/2at^2 for the officer
remember u = 0 because the officer starts from rest.
Distance = 1/2 * 1 * t^2

Now, for the officer to reach the motorist, their distances must be the same.

Hence 1/2 * t^2 = 16.5 * t
or t^2 = 33t

So there are two solutions.
Either t = 0s which is obvious
or t = 33 seconds (by cancelling), which is the one you want.

So we now know it takes 33 seconds for the officer to reach the motorist.

To get the speed, just use v = u + at
v = 0 + 1 * 33 = 33 m/s

Now, the last part is similar:
Just stick this back in the formula for the distance
s = 1/2 * 1 * 33^2
and we get a distance of 544.5m.

Hope this helps you.

Answer 2

Hints:
s = at²/2 s = distance, a = acceleration, t=time
s=vt s=distance, v=velocity, t=time
v=at v = velocity, a=acceleration, t=tome


Now quite screwin' off and get busy doin' yer homework.


Doug