A time dependent force `F=6t` acts on a particle of mass `1kg`. If the particle starts from rest, the work done by the force during the first `1 sec.` will be

Options

A. 4.5 J
B. 22 J
C. 8 J
D. 18 J

Answer

A

Explanation

Given F = 6 t
`m (dv)/(dt) = 6t`
` int_(v=0)^(v) dv = int_(t=0)^(t=1 "sec") 6tdt " " (m=1 kg)`
` v = 6/2 `m/s = 3m/s
From work -energy therm
`W = 1/2mv^(2) -1/2m(0)^(2)`
`W=1/2xx1(3)^(2)=4.5 J `