5. You are late to class and speeding on the highway. Unfortunately, you pass a

Question

5. You are late to class and speeding on the highway. Unfortunately, you pass a police officer with a radar gun, who measures your speed to be 80 mph. At the exact instant that you pass the police vehicle, the officer begins accelerating at a steady rate of 10 mph/s, while you continue on down the road at the same speed. Determine the following and use two significant figures for all responses:

A. How much time elapses before the police cruiser is travelling at the same speed as you?

B. What is the distance between the two vehicles at that time?

C. How much time elapses before the police cruiser catches up to you?

D. What is the police officer’s speed at this time?

Explanation / Answer

1mph = 0.4480 m/s

so 70 mph = 70* 0.4470

= 31.29 m/s

so

xm = spped * time

Xm = 31.29 t

x police = 1/2 a t^2

Xp = 0.5*2*t^2 = t^2

x mototrist = x police

t^2 = 31.29 t

t = 31.29 secs

-----------------------

b. x mototrist = 31.29 t

X m = 31.29 * 31.29

XM = 979 m or nearly 1 km

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C. asV = u + at

t = 31.29/(10* 0.4470)

t = 7 secs

--------------------------------

d. V = a t = (10*0.4470* 7

v = 31.29 m/s

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