a drunken motorist who is moving at a constant velocity of 90 km/h passes a stationary police patrol car. The patrol car immediately gives chase at a constant acceleration and catches up with the motorist after a distance of 10 km. Calculate the time taken by the patrol car to catch up with the motorist.

Question

a drunken motorist who is moving at a constant velocity of 90 km/h passes a stationary police patrol car. The patrol  car immediately gives chase at a constant acceleration and catches up with the motorist after a distance of 10 km. Calculate the time taken by the patrol car to catch up with the motorist.

drwls · Accepted Answer

Start counting time t from when the drunk motorist passes. Let his distance travelled be X1 and the distance travelled by the police car be X2.

X1 = V*t

X2 = (a/2) t^2

X1 = X2 when both equal 10 km. That is when the police car catches up.

t = 10 km/(90 km/h) = 1/9 h = 6.67 minutes

You could also solve for the police car's acceleration a, but they don't ask for that.