Question

A car starts from rest on a half kilometer long bridge. The coefficient of friction between the tyre and the road is 1.0. Shwo that one cannot drive through the bridge in less tahn 10 s.

Answer 1

Let a maximum acceleration is produced in car.
$ma=\mu R$
(For more accelerations the tyres will slip]
$\Rightarrow ma=\mu mg\Rightarrow a=\mu g=1\times 10=10m/s^2$
For crossing of the bridge in minimum time, it has to travel with maximum acceleration.
$u=0,S=500,a=10m/sFromS=ut+\frac{1}{2}a{t}^{2}500=0+\left(\frac{1}{2}\right)10t^2\Rightarrow t=\sqrt{100}=10sec.$

If acceleration is less tahn $10m/s^2$ time will be more than 10 sec. So one can't drive through the bridge in less than 10 s.