4) A police officer hidden at an intersection observes a car that ignores a stop

Question

4) A police officer hidden at an intersection observes a car that ignores a stop sign, crosses the intersection, and continues on at a constant speed. The police officer takes off in pursuit as soon as it passed the stop sign, accelerating at 6.2m/s/s until her speed is 80m/s, and continues at this speed until she catches the car. (so there are two parts of the cop’s motion which add up)

The police officer catches the car at a total distance of 1.4km from the intersection.

How fast was the car traveling? How long does it take to catch the car?

Explanation / Answer

For Police:

v=u+at

80 = 0+ 6.2 t1

t1=12.90 s

distance:

V^2 = U^2+2 a s1

80^2= 0+ 2* 6.2* s1

s1=516.12 m

Second part:

s2= U* t2

(1400-516.12)= 80* t2

t2=11.04 s

Car speed:

V= d / (t1+t2) =1400/(12.90+11.04) = 58.47 m/s

TIme taken to catch car:

T= t1+t2 =12.90+11.04 =23.94 s

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