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

Answer

3

Explanation

s"`=(v^(2))/(2(f//2))`
but `s=(v^(2))/(2f) :.`s"`=2s`
and s'`=12s`
and `12s=vt " "...(1)`
and `v^(2)=2fs " "...(2)`
from (1) and (2)
`144s^(2)=(2fs).t^(2)`
`:.s=(ft^(2))/(72)`