A body of mass m has an initial speed v is acted by two forces `vec(F)_(1)` and `vec(F)_(2)`. After something work done by `vec(F)_(1)` is `-1/2 mv^(2)` and speed of the body is 2v. Then, the work done by `vec(F)_(2)` is

Options

A. `3/2 mv^(2)`
B. `mv^(2)`
C. zero
D. `2mv^(2)`

Answer

D

Explanation

`W_(1)+W_(2)=1/2 m(2v)^(2)-(v)^(2)`
`-1/2 mv_(2)+W_(2)=3/2 mv^(2)`
`W_(2)=2mv^(2)`