Question

A speeding motorist travels with a constant speed of 15 m/s on a straight road. At time t = 0, he passes a hidden police car which is at rest. The instant that the motorist passes, the police car begins accelerating at a constant rate of 2 m/s2 in order to catch the motorist.
a)How many seconds pass before the police car reaches the motorist?
b)How fast is the police car moving when it reaches the motorist?
c) How much distance has the police car traveled when it reaches the motorist?

Answer 1

car location x = 0 + 15 t
police x = (1/2) 2 t^2
so
15 t = t^2
t = 0 (of course) and t = 15 seconds
v = a t = 2 * 15 = 30 m/s
x = (1/2)2 (225) = 225 meters
or since the car went the same distance as the police car
x = 15 m/s * 15 s = 225 meters