A motorcycle officer hidden at an intersection observes a car driven by an obliv

Question

A motorcycle officer hidden at an intersection observes a car driven by an oblivious driver who ignores a stop sign and continues through the intersection at constant speed. The police officer takes off in pursuit 1.68 s after the car has passed the stop sign. She accelerates at 4.6 m/s2 until her speed is 104 km/h, and then continues at this speed until she catches the car. At that instant, the car is 1.7 km from the intesection (a) How long did it take for the officer to catch up to the car? (b) How fast was the car traveling? mi/h

Explanation / Answer

104 km/hr=28.889 m/s

part a:

initial speed of the officer=u=0

acceleration=4.6 m/s^2

final speed=104 km/hr=28.889 m/s

then time taken to reach this speed=(final speed-initial speed)/acceleration

=6.28 seconds

distance travelled in this duration=(final speed^2-initial speed^2)/(2*acceleration)

=90.715 m

for the rest of the distance(1700 m -90.715 m=1609.3 m) she travels with a speed of 28.889 m/s

time taken=1609.3/28.889=55.706 seconds

so total time taken=6.28+55.706=61.986 seconds

part b:

total time travelled by the car=61.986+1.68=63.666 seconds

distance travelled=1700 m

then speed of the car=distance/time=26.702 m/s

=59.73 mi/hr

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