A car moving with a velocity `6.25 ms^(-1)` is decelerated with `2.5sqrt(v) ms^(-2)` (v is instantaneous velocity). Time taken by the car to come to rest is

Options

A. 2s
B. 3s
C. 2.5s
D. 4s

Answer

A

Explanation

Given, `u = 6.25 ms^(-1)` and `a = -2.5 sqrt(v) ms^(-2)`, v = instaneous velocity
As we know,
`a = (dv)/(dt)`
So, `(dv)/(dt) = -2.5sqrt(v)`
Integrate on the both sides, we get
`rArr int_(6.25)^(0) (1)/(sqrt(v)) dv = -2.5 int dt`
`rArr [2sqrt(v)]_(6.25)^(0) = -2.5t`
`rArr t = (2 xx 2.5)/(2.5) = 2s`
Hence, the correct option is (a).