Two cars started moving with initial velocities v and 2v. For the same deceleration, their respective stopping distances are in the ratio

Options

A. A)`1:1`
B. `B)1:2`
C. `C)1:4`
D. `D)2:1`

Answer

C

Explanation

For first car
`v_(1)^(2)=u^(2)-2as`
`0=v-2as_(1)`
`s_(1)=(v)/(2a)`
`s_(1)=(v)/(2a)`
For second car
`v_(2)^(2)=u^(2)-2as`
`0=(2v)^(2)-2as_(2)`
`s_(2)=(2v)/(a)`
`therefore (s_(1))/(s_(2))=((v)/(2a))/((2v)/(a))`
`therefore (s_(1))/(s_(2))=(1)/(4)`