An automobile travelling with a speed `60 km//h` , can brake to stop within a distance of `20 m` . If the car is going twice as fast i. e. , `120 km//h`, the stopping distance will be

Explanation

Let us suppose that when the brakes are applied, the automobile does not skid. To get the maximum stopping distacne (s), we take the ffirctional force (f) between the tyres and the road to a maximum. The work done by the frictiional force must be equal to the change in the kinetic energy of the automobile. if `upsilon` is the initial speed of the automobile,
`fs = (1)/(2) mupsilon^2 or s = (m upsilon^2)/(2f)`
If we assume f to be the same for two initial speeds `(upsilon_1 and upsilon_2)`,
`s prop upsilon^2 or (s^2)/(s_1) =((upsilon_2)/(upsilon_1))^2 or s_2 = ((upsilon_2)/(upsilon_1))^2 s_1`
As `upsilon_2 = 96km//h, upsilon_1 = 48 km//h and s_1 = 40 m, s_2 = ((96km)/(48))^2 xx40`
=160m