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^(2)`.

Options

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

Answer

D

Explanation

` (ft_1)/(t_2 -(t_1+t)) =(f)/(2) rArr t_2 = 3t_1+t `
` (1)/(2) (ft_1) (t_1) =S " "…(i) `
`(1)/(2) ft_1 (t+t_2) = 155`
`(1)/(2) ft_1(2t+3t_1) =155`
(i) divided (ii)
`(t_1)/(2t+3t_1)=(1)/(15) " "rArr " " t_1 =(t)/(6) , S=(1)/(2) ft_1^(2) =(1)/(72) ft^(2) `