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 39.0 m/s. When it is 70 m behind you and moving with a velocity of 44.5 m/s, the police car starts to slow down. The police need to have the same velocity as you when they catch you. What acceleration must the police car have so that its velocity matches yours when it catches up to you? Give your answer in m/s2, but do not include the units in your answer. Be careful with the sign of your answer. Signs matter. 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

In that frame, the police car is advancing toward you at (44.5 - 39) = 5.5 m/s and is 70 m away from you.

Using

v^2 = u^2 + 2ad, where v = 0,

a = -u^2 / 2d = - (5.5m/s)^2 / (2*70m) = - 0.216 m/s^2

The time it takes to slow down is

t = delta v /a = - 5.5m/s / -0.216m/s^2 = 25.46 s

during which you've advanced

s = 39.0m/s * 25.46 s = 992.94 m

and the police

S = 44.5m/s*25.46 s - (1/2) * 0.216m/s^2 * (25.46s)^2 = 1062.96 m

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