A force given by the relation F = 8t, acts on a body of mass 2 kg, initially at rest. Find the work done by this force on the body during first 2 seconds of its motion

Options

A. 64 J
B. zero
C. `- 64 J`
D. none of these

Answer

A

Explanation

`F = 8t`
`m (dv)/(dt) = 8t`
`m underset(0)overset(v)int dv = 8 underset(0)overset(t)int t dt`
`mv 4t^(2)`
or `m = (dx)/(dt) = 4 t^(2)`
`rArr dx = (4 t^(2))/(m) dt = 2t^(2) dt`
`W = int Fdx = underset(0)overset(v)int (8 t xx 2 t^(2)) dt = 64 J`