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

Answer

80

Explanation

`(1)/(2) mv ^(2) = Fs, (1)/(2) mv _(1) ^(2) = F s _(1)`
`(1)/(2) mv _(2) ^(2) = Fs _(2)`
`therefore (v _(1) ^(2))/( v _(2) ^(2)) = (s _(1))/( s _(2)), As v _(2) = 2v _(1)`
`therefore ( v _(1) ^(2))/( 4 v _(1)^(2)) = (s _(1))/ (s _(2))= (20)/( s _(2)), s _(2) =80 m`