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.
physics - drwls, Friday, November 2, 2012 at 8:48am
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.