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Acceleration of a particle moving in x-y...

Acceleration of a particle moving in x-y plane varies with time t as
`a = (t hat(i) + 3t^(2) hat(j))`
Here a is in `m//s^(2)` and t in second. At time t = 0, particle is at rest at origin. Mass of the particle is 1 kg. Find the net work done on the particle in first 2 s.

A

`40 J`

B

`34 J`

C

`16 J`

D

`48 J`

Text Solution

Verified by Experts

The correct Answer is:
B
`(d vec(v))/(dt) = ti + 3t^(2)j :. int_(o)^(v )d vec(v ) = int_(o)^(2)(ti + 3t^(2)j)dt`
`:. vec(v ) = (2i + 8j)m//s`
`:. v = sqrt68`
by work energy theorem `:. w = (1)/(2)mv^(2) :. w = 34J`
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