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

Answer

A

Explanation

For the first part of journey,
`S_(1) =1/2 ft_(1)^(2) = S " "( :. u = 0 ) " "...(i)`
and `v=ft_(1)`
For the second part of journey , `S_(2) =vt`
or `S_(2) = ft_(1) t " "` (Using (ii))
For the third part if journey
`S_3=v^2/(2(f/2))=v^2/f=(ft_1^2)/f=ft_(1)^2" "` (Using(ii))
or `S_(3) = 2 S_(1) =2 s " "` (Using (i))
As `S_(1) +S_(2) +S_(3) = 5 S " "` (Given
`:. S + ft_(1) t + 2S = 5 S " or " ft_(1)t = 2S" "...(iii)`
Divide (i) by (iii) , we get, `S/(2S) = (ft_1^2)/(2xxft_(1)t)" or "t_1 =t`
`:. S = 1/2 ft_(1)^(2) =1/2 ft^(2)`