Question

A motorist traveling with a constant speed of 15m/s passes a school-crossing corner, where the speed limit is 10m/s. Just as the motorist passes, a police officer on a motorcycle at the corner starts off in pursuit with constant acceleration of 3m/s^2. (a)How much time elapses before the police catches up the motorist? (b)What is the officer's speed limit at that point? (c)What is the total distance each vehicle has traveled at that point?

Answer 1

a) s1= vt - for motorist
s2= (1/2)*a*t^2 - for police officer

when the cop cathes up the motorist:
s1 = s2

So vt = (1/2)*a*t^2
15*t= (1/2)*3*t^2
t = 15*2/3 = 10 sec
b) v = u + a*t
= 0 + 3*10 = 30 m/s
c) distance s1=s2= 15*10 = 150m