A car , starting from rest, accelerates at the rate `f` through a distance `S` then continues at constant speed for time `t` and then decelerates at the rate `(f)/(2)` to come to rest . If the total distance traversed is `15 S` , then

Options

A. `d=1/2alphat^(2)`
B. `d=1/4alphat^(2)`
C. `d=1/72alphat^(2)`
D. `d=1/6alphat^(2)`

Answer

C

Explanation

`A` to `B: v^(2)=2 alpha d_(1)=2 alpha d`
`C` to `D: 0=v^(2)-2alpha/2d_(3)impliesd_(3)=2d`
`d_(3)=2d`
`d_(1)+d_(2)+d_(3)=15 dimpliesd_(2)=12d`
`B` to `C: d_(2)=12d=vtimplies v=(12d)/t`
`A` to `B: v^(2)=2alphadimplies((12d)/t)^(2)=2alphad`
`(144d^(2))/t^(2)=2alphad`
`d=1/72 alpha t^(2)`