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 travelled is 15 s, then

Options

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

Answer

D

Explanation

Distance from A to B `= S = (1)/(2) ft_(1)^(2)`
Distance from B to C= `(ft_(1))t`
Distance from C to D `= (u^(2))/(2a) = ((ft_(1))^(2))/(2(f//2))= ft_(1)^(2) = 2S`

`rArr S+ f t_(1)t + 2S= 15S`
`rArr f t_(1)t= 12S` …(i)
`(1)/(2) f t_(1)^(2)= S` ...(ii)
Dividing (i) by (ii), we get `t_(1) = (t)/(6)`
`rArr S= (1)/(2) f ((t)/(6))^(2) = (f t^(2))/(72)`