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. `S=ft`
B. `S=(1)/(6)ft^(2)`
C. `S=(1)/(72)ft^(2)`
D. `S=(1)/(4)ft^(2)`

Answer

C

Explanation

`{:(V^(2)-O^(2)=2fs),(O^(2)-V^(2)=-2(f)/(2)S_(3)):}}®S_(3)=2S`
`:. S_(2)=12s, 12s=vt` also `V=sqrt(2fs)`
`:. 12S=sqrt(2fs),144s^(2)=2fs.,s=(1)/(72)ft^(2)`