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.

#### Solution

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/s^{2}

To cross the bridge in minimum possible time, the car must be at its maximum acceleration.

u = 0, s = 500 m, a = 10 m/s^{2}

From the equation of motion,

`s=ut+1/2at^2`

Substituting respective values

`500=0+(1/2)10t^2`

`=>t=sqrt100=10`s

Therefore, if the car's acceleration is less than 10 m/s^{2}, it will take more than 10 s to cross the bridge. So, one cannot drive through the bridge in less than 10 s.