Power applied to a particle varies with time as `P =(3t^(2)-2t + 1)` watt, where t is in second. Find the change in its kinetic energy between time `t=2s` and `t = 4 s` .

Options

A. 32 J
B. 46 J
C. 61 J
D. 102 J

Answer

B

Explanation

Instantaneous power is , `P = (d (K))/(dt)`
So, change in K.E. can be written
as `K . E _(f) - K . E _(i) = int _(t _(1)) ^( t _(2)) Pdt`
`Delta K. E . = int _(2) ^(4) ( 3t ^(2) - 2t +1) dt`
`= (t ^(3) - t ^(2) +t) _(2) ^(4) = 46 J`