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A car traveling at a constant speed of 30m/s passes traffic police on a motorcycle hidden behind a tree. Two seconds after the speeding car passes, the police set out to catch the car, accelerating at a constant rate of 6m/s2.

How far does the police travel until he catches the speeding car?

Give your answer in [m].

Answer :

Answer:

411.37 meters

Explanation:

car position = 60 + 30 t

cop position = 1/2 a t^2 =   3 t^2     equate them

30t + 60 = 3t^2      re-arrange

3t^2 - 30t - 60 = 0    use quadratic formula to find t = 11.71 sec

1/2 (6)(11.71)^2 = 411.37 meters

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