A car starts from rest with an acceleration of ` 6 m//s^(2) ` which decreases to zero linearly with time, in 10 seconds, after which the car continues at a constant speed. Find the time required for the car to travel 400 m from the start

Options

A. ` 16.67s`
B. ` 25.6 s`
C. `10.56 s `
D. `9.56 s`

Answer

A

Explanation

`rArr (a)/(6) +(t)/(10) =1 rArr a= 6 (1-(t)/(10 )) rArr (dv)/(dt) = 6(1-(t)/(10))`
` int _0^(v) dv =int _0^(t) 6(1-(t)/(10 )) dt rArr v= 6 (t-(t^(2))/(20)) rArr v= 30 m //s at `the end of 10 sec .
` int _0^(x) dx = int _0^(t) 6 ( t-(t^(2))/(20) ) dt rArr x= 6 ((t^(2))/(2) -(t^(3))/(60)) `
` x= 200 m ` at the end of 10 sec .` rArr` remaining 200 m is covered with constant speed of ` 30m//s `
`rArr `further time taken = 200//30 =6.67 " "rArr ` total time for 400 m =16.67 sec