Question

A motorist traveling with constant speed of vc = 17.000 m/s passes a school-crossing corner, where the speed limit is 10 m/s. Just as the motorist passes, a police officer on a motorcycle stopped at the corner starts off in pursuit. The officer accelerates from rest at am = 3.190 m/s2 until reaching a speed of 25.500 m/s. The officer then slows down at a constant rate until coming alongside the car at x = 346.000 m, traveling with the same speed as the car.

Consider a coordinate system with origin at the school-crossing corner, x=0, and the +x-axis in the direction of the car's motion.

(a) How long does it take for the motorcycle to catch up with the car (in s)?

(b) How long does it take for the motorcycle to speed up to 25.500 m/s? (Express your answer in s.)

(c) How far (in m) is the motorcycle from the corner when switching from speeding up to slowing down?

(d) How far (in m) is the motorcycle from the car when switching from speeding up to slowing down?

(e) What is the acceleration (in m/s2) of the motorcycle when slowing down? (pay attention to the sign)