A car starts from rest on a ` 2 - km` long bridge. The coefficient of friction is `0.5`. Find the minimum time to cross the bridge.

Explanation

Due to friction , the car accelerates on the road.
`f_(max) = mu N = mu mg`
Maximum acceleration on road ` = (f_(max))/(m) = mu g`
`s = ut + (1)/(2) at^(2)`
`2000 = 0 + (1)/(2) a_(max) t^(2) = (1)/(2) mu g t^(2) = (1)/(2) xx 0.5 xx 10 t^(2)`
`t^(2) = (2000)/(2.5) = 800`
`t = t_(min) = 20 sqrt(2) s`