A car, starting from rest, accelerates at the rate (f) through a distance (S), then continues at constant speed for some time (t) and then decelerates at the rate ` f//2` to come to rest. If the total distance is ` 5 S`, then prove that
` S=1/2/ ft^(@)`.

Explanation

During accleration of object,
` u=0, a= f, S=S, v=v_(1)`
As, ` v^(2) =u^(2) + 2 S so v_(1)^(2) =0^(2) + S=2 f S`
or ` v_(1) =sqrt 2 f S`
During unufirn nyufirn nituib if ibhect,
`u =v_(1) =sqrt 2 f S, t=t,`
Distanc etravelled , ` S_(1) =ut =sqrt 2 f S. t`
During deceleration of object, ` u =sqrt 2 d S, a=- f//2 u=0, S=S_(2)`
As, ` v^(2) -u^(2)=2 S`
so ` 0- (sqrt r f S0^(2) =2 (-f//2) S_(2)) S_(2) or S_(2) =2 S`
Given `S+S_1+S_2=5S`
or `S+sqrt(2fSt)+2S=5S`
or `sqrt(2fS)t=2S` or `S=1/2ft^2`