An impulse `vrc(I)` changes the velocity of a particle from `vec(v)_(1)` to `vrc(v)_(2)`. Kinetic energy gained by the particle is :-

Options

A. `(1)/(2)vec(I) .(vec(v)_(1) + vec(v)_(2))`
B. `(1)/(2)vec(I).(vec(v)_(1) - vec(v)_(2))`
C. `vec(I).(vec(v)_(1) - vec(v)_(2))`
D. `vec(I).(vec(v)_(1) + vec(v)_(2))`

Answer

A

Explanation

`DeltaKE = (1)/(2)mv_(2)^(2) - (1)/(2)mv_(1)^(2)`
`= (1)/(2)m(vec(v)_(2) - vec(v)_(1)) = (1)/(2) vec(I).(vec(v)_(1) + vec(v)_(2))`