Consider a police car catching you from behind to pull you over for speeding. Yo

Question

Consider a police car catching you from behind to pull you over for speeding. You are driving at a constant velocity of 37.0 m/s. Initially, at t = 0, the police car is 75 m behind you and moving with a velocity of 42.3 m/s. The police car starts to slow down at that time so that they have the same velocity as you when they catch you. How much time does it take for the police to catch you? Give your answer in seconds, but do not include the units in your answer. You should give your answer to at least three significant figures. Your answer won't be graded on the number of significant figures. Giving your answer to three or more significant figures will keep it from being counted as incorrect due to rounding.

Explanation / Answer

Let 't' be the time taken by the police to catch

Acceleration of the police car = (37 - 42.3)/t = -5.3/t

Distnace covered by the police car in t sec (dp)= (42.3)(t) + (1/2)(-5.3/t)(t2) = 39.65t

Distance covered by you in t sec (dy) = (37)(t)

According to the given conditions,

ds = dy + 75

=> 39.65t = 37t + 75

=> t = 28.302

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