Question

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

Answer 1

Distance = 0.5 km. = 500 m.

The question is asking that car cannot derive in less than 10 seconds. It means that it will be the minimum time. It means the Minimum Force must be acting for the minimum time.

Let us Prove it by mathematics expressions.  (Okay.)

friction (limiting) = ma [When Force is minimum

⇒ μmg = ma

∴ a = μg

⇒ a = 1 × 10

∴  a = 10 m/s².

Now,  u = 0,

S = ut + 1/2 × at²

⇒ 500 = 1/2 × 10 × t²

⇒  t² = 100

⇒ t = 10 seconds.

This will be the minimum time, since, force applied is also minimum. A Force cannot be less than as applied on it. Because if force will be less than I written than body will not move because of the Friction.

Hope it helps.