A body of mass `1 kg` begins to move under the action of a time dependent force `vec F = (2 t hat I + 3 t^(2) hat j) N`, where `hat i` and `hat j` are unit vectors along x-and y-axes. What power will be developed by the force at the time `t` ?

Options

A. `(2t^(3) + 3t^(5))W`
B. `(2t^(2) + 3t^(3))W`
C. `(2t^(2) + 4t^(4))W`
D. `(2t^(3) + 3t^(4))W`

Answer

`(1)`

Explanation

M = 1 kg
` a = F/M = (2t)(1) hat i + (3t^(2))/(1) hat j`
`V = int a dt = int 2t dt hat i + int 3t^(2) dt hat j`
`V = t^(2)hat i + t^(3) hat j`
`Power = vec F. Vec V = (2t hat i + 3t^(2)hat j ).(t^(2)hat i + t^(3) hat j)`
Power = `2t^(3) + 3t^(5)`