Speeds of two identical cars are u and 4u at at specific instant. The ratio of the respective distances in which the two cars are stopped from that instant is

Options

A. `1 : 1`
B. `1 : 4`
C. `1 : 8`
D. `1 : 16`

Answer

D

Explanation

Using work - energy theorem
`W_("total") = Delta K`
i.e.., work done by stopping forces should be equal to change in the kinetic energy of car.
`-F_("stopping") xx "stopping distance" = (k_("final") - k_("initial"))`
`rArr -F_("stopping") xx s=(0 -(1)/(2)mv_("initial")^(2))`
`rArr F_("stopping") xx s = (1)/(2) mv_("inital")^(2)`
As stopping force is same for both the cars, hence
`s prop v_("initial")^(2)`
`rArr (S_(1))/(S_(2)) =((v_("initial")^(2))_(1))/((v_("initial")^(2))_(2)) = (u^(2))/((4u)^(2)) = (1)/(16)`.