A car initiates its motion from rest on a half kilometer long bridge. The coefficient of friction between the tyre and the road is 1.0 . Determine the minimum possible time required to drive through the bridge.

Step-by-step solution

The maximum acceleration of the car is provided by the frictional force between the tyres and the road. f_ max = N = mg ma_ max = mg a_ max = g Substituting the given values = 1.0 and taking g = 10 m/s ^2 : a_ max = 1.0 10 = 10 m/s ^2 The car starts from rest, so the initial velocity u = 0 . The length of the bridge is s = 0.5 km = 500 m . Using the equation of kinematics to find the minimum time t : s = ut + 1 2 a_ max t^2 500 = 0 + 1 2 (10) t^2 5 t^2 = 500 t^2 = 100 t = 10 s