A body of mass `m`, moving along the positive x direction is subjected to a resistive force `F = Kv^(2)` (where K is a constant and `v` the particle n velocity). If `m = 10 kg v = 10 m//s` at `t = 0, " and " K = 2N (m//s)^(-2)` the velocity when `t = 2s` is:

Options

A. `(10)/(3) m//s`
B. `2 m//s`
C. `- (10)/(3) m//s`
D. `(3)/(10) m//s`

Answer

B

Explanation

`F = - k v^(2)`
`m (dv)/(dt) = - kv^(2)`
`underset(10)overset(v)int (dv)/(v^(2)) = - (k)/(m) underset(0)overset(t)int dt`
`- |(1)/(v)|_(10)^(v) = (2)/(10) |t|_(0)^(t)`
`(1)/(v) - (1)/(10) = (1)/(5) (2)`
`v = 2 m//s`