At any instant the speeds of two identical cars with the same retardation are u and 4u, starting from that instant the respective distances the cars travel before stopping are in the ratio

Options

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

Answer

D

Explanation

The final velocity of both the cars v = 0
Let the first and the second cars travel distances `d_(1)` and `d_(2)` before coming to rest. If the retardation of both the cars is a then in case of the first car,
`-u^(2) = -2ad_(1)" ""or",d_(1) = (u^(2))/(2a)`
in case of the second car,
`-(4u)^(2) = -2ad_(2)" ""or", d_(2)= (8u^(2))/(a)`
`:.(d_(1))/(d_(2))=(u^(2))/(2a).(a)/(8u^(2))=(1)/(16)`
Hence `d_(1) : d_(2) = 1:16`