A car starts from rest and moves on a surface in which the coefficient of friction between the road and the tyres increases linearly with distance (x). The car moves with the maximum possible acceleration. The kinetic energy (E) of the car will depend on x as 

Options

A. `E prop 1/(x^2)`
B. `E prop 1/x`
C. `E prop x`
D. `E prop x^2`

Answer

D

Explanation

`a = v (dv)/(dx) = mu g = (alpha x) g`, where `alpha` = constant
or `int_0^v vdv = int_0^x alpha g x dx " or " 1/2 mv^2 = 1/2 m alpha g x^2 " or " E prop x^2`.