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An impulse vrc(I) changes the velocity o...

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 :-

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))`

Text Solution

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The correct Answer is:
A
`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))`
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