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

Options

A. 9 J
B. 18 J
C. `4.5` J
D. 22 J

Answer

C

Explanation

F = 6t
` :. "ma = 6t`
` :. A = (6t)/m = (6t)/m = 1 = 6t`
` :. (dv)/(dt) = 6t`
` :. "dv = 6t dt"`
` :. Int_(0)^(v) dv - 6 int_(0)^(1) " t dt "`
` = 6 xx1/2[ :. t = 1 ] `
= 3 m/s
` W = 1/2 mv^(2) - 1/2 mv_(0)^(2)`
` = 1/2 xx1xx9-0`
`= 4.5 J `