Question

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

Answer 1

Let a be the maximum acceleration of the car for crossing the bridge.



From the above diagram,
ma = μR
(For more accelerations the tyres will slip)
ma = μmg
a = μg = 1 × 10 = 10 m/s²

To cross the bridge in minimum possible time, the car must be at its maximum acceleration.
u = 0, s = 500 m, a = 10 m/s²

From the equation of motion,
$s=ut+\frac{1}{2}a{t}^2$
Substituting respective values
$$\begin{gathered} 500=0+\left(\frac{1}{2}\right)10t^2 \\ \Rightarrow t=\sqrt{100}=10\mathrm{s} \end{gathered}$$
Therefore, if the car's acceleration is less than 10 m/s², it will take more than 10 s to cross the bridge. So, one cannot drive through the bridge in less than 10 s.