Question

A motorist drives along a straight road at a constant speed of 15.0 m/s. Just as she passes a parked
motorcycle police officer, the officer starts to accelerate at 2.00 m/s2
to overtake her. Assuming the
officer maintains this acceleration, (a) determine the time it takes the police officer to reach the
motorist. Also, find (b) the speed and (c) the total displacement of the officer as he overtakes the
motorist.
a. (a) 15.0 s; (b) 30.0 m/s; (c) 225 m
b. (a) 7.50 s; (b) 30.0 m/s; (c) 169 m
c. (a) 3.75 s; (b) 7.50 m/s; (c) 56.3 m
d. (a) 7.50 s; (b) 15.0 m/s; (c) 113 m

Answer 1

Xm = v*t = 15*t
Xcop = 0.5*a*t^2 = 0.5*2*t^2 = t^2

When he overtakes motorist: Xm = Xcop --> 15*t = t^2 --> t = 15.0 s

Speed of cop: v = a*t = 2*15 = 30 m/s

Position of cop and motorist: Xcop = 15^2 = 225 m