The displacement `x` of a particle of mass `m` kg moving in one dimension, under the action of a force, is related to the time t by the equation `t=4x+3` where `x` is in meters and `t` is in seconds. The work done by the force in the first six seconds in joules is

Options

A. 9 J
B. 6 J
C. 0 J
D. 3 J

Answer

C

Explanation

`x = (t-3)^(2) rArr v = (dx)/(dt) = 2(t-3)`
at `t = 0, v_(1) = -6m//s` and at t = 6 sec, `v_(2) = 6m//s`
so, change in kinetic energy `= W = (1)/(2) mv_(2)^(2) - (1)/(2) mv_(1)^(2) = 0`