When a `2` kg car driven at `20 m//s` on a level road is suddenly put into netural gear (i.e. allowed to coast), the velocity decreases in the following manner:
`V=20/(1+(t/20))m//s`
Where t is time in sec. The deceleration of car at the instant its speed is `10 m//s` is.

Options

A. `1//4 m//s^(2)`
B. `1//2 m//s^(2)`
C. `1 m//^(2)`
D. `3//4 m//s^(2)`

Answer

A

Explanation

Given that initial velocity `=u=20 m//s`
`v=20/(1+t/20)`
at `u=10 m//s`
`10/1=20/(1+t/20)`
`2=1+t/20`
`t=t/20`
`t=20` sec
From `u=20/(1+t/20)=400/(20+t)`
acceleration `a=(dv)/(dt)=400xx1/((20+t)^(2))`
acceleration `a=(-400)/(40xx40)`
acceleration `a=(-1)/4 m//s^(2)`
so deceleration `a=1/4 m//s^(2)`