A police officer on a motorcycle is hiding behind a bush by a stop sign. A motor

Question

A police officer on a motorcycle is hiding behind a bush by a stop sign. A motorist driving at a constant velocity runs through the stop sign without slowing down and continues to drive at that constant velocity vo. Right at the moment the motorist passes through the stop sign, the officer begins to chase the motorist with a constant acceleration a.

a) In terms of vo and/or a, at what distance from the stop sign will the officer catch up with the motorist?

b) In terms of vo and/or a, what is the speed of the officer the moment he catches up with the motorist?

Explanation / Answer

a)

let the distance be "d"

for the motorist

d = Vo t

t = d/Vo                        eq-1

For the officer :

d = (0.5) at2

t = sqrt(2d/a)                  eq-2

using eq-1 and eq-2

sqrt(2d/a) = d/Vo

2d/a = d2/Vo2

d = 2Vo2 /a

b)

V = at = a d/Vo = (a/Vo) (2Vo2 /a) = 2 Vo

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