On a horizontal rought rood , value of coefficient of friction `mu =0.4`.Find the minimum time in which a distance of `400m` can be covered. The car start from rest and finally comes to rest.

Explanation

Maximum friction on horizontal rough road ,`f_(max) =mumg`
`:.` Maximum acceleration or retardation of the car may be
`a_(max)` or `a =(f_(max)) /(m) = (mumg)/(m) =mug`
` =0.4xx10=4m//s^(2)`
Let , the rest car acceleration and retards for time 't' with `4m//s^(2)`
Then, `(1)/(2) at^(2)+(1)/(2) at^(2)=400m`
or `at^(2) =400m` or `4t^(2) =400`
or `t =10s`
Therefore the minimum time is `20s(10s` of acceleration and `10s`of retardation).