A car starts with a velocity of `100m//s` on a half kilometre long bridge The coefficient of friction between the tyres and road is `0.1` Show that one cannot drive throught the bridge in less than `10 s` Take `g = 10m//s^(2)`.

Explanation

Here,` u = 100m//s, s = (1)/(2)km = 500m`
`mu = 1.0`
If a is the retardation due to friction, then
`a = - mu g = - 1.0 = - 10ms^(-2)`
From `s = ut + (1)/(2)a t^(2)`
`500 = 100 t-5 t^(2) or t^(2) - 100 t + 500 = 0`
or `t^(2) - 20 t + 100 = 0`
or`t = (20 +- sqrt(400 - 400))/(2) = 10s`
Clearly time cannot be less than 10.0 s.