Your good friend\'s car ignores a stop sign and enters an intersection with a sp

Question

Your good friend's car ignores a stop sign and enters an intersection with a speed of 31.6 m/s. He then continues with a constant velocity. A motorcycle patrol officer is parked at the intersection. He discards his hot cocoa and doughnut and begins accelerating (at the instant the car passes him) with a constant acceleration of
3.29 m/s^2.
(a) How long (s) does it take the officer to catch the car?
(b) How far (m) has the officer traveled when he catches up to the car?
(c) How fast (m/s) is the officer going when he catches up to the car?

Explanation / Answer

Let they meeet after travelling a distance "d" and time "t"

distance travelled by friend, d = ut = 31.6t

distance travelled by officer, d = at2/2 = 3.29t2/2 = 1.6t2

1.6t2 = 31.6t

t = 31.6/1.6 = 19.2

(a) it takes 19.2s for the officer to catch the car

d = 31.6t = 607.02

(b) the officer traveled 607.02 m when he catches up to the car

v = u+at

v = 0 + 3.29*19.2

v = 63.17

(c) the speed of officer when he catches up to the car is 63.17 m/s

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