A car is travelling on a straight road. The maximum velocity the car Can attain is `24 ms^-1.` The maximum acceleration and deceleration it can attain are `1 ms^-2` and `4 ms^-2` respectively. The shortest time the car takes from rest to rest in a distance of 200 m is,

Options

A. `22.4 s` (b) 30 s (c) 11.2 s (d) 5.6 s
B. `30 s`
C. `11.2 s`
D. `5.6 s`

Answer

A

Explanation

Declaration is four times. Therefore, deceleration
time should be `1/4 th.`

`v_(max)=(a_1)(4t)=(1)(4t)=4t`
Area of v-t graph=displacement
`:. 200=1/2(5t)(4t)`
or `t=sqrt20 s`
Total journey time=`5t=22.4s`