Question

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

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

Answer 1

The correct option is D 4.5 J

Given,

$F=6t$

$m=1kg$

Force, $F=ma=6t$

$1\times \frac{dv}{dt}=6t$

$dv=6tdt$

Integrating both side,

$v=\int dv={\int }_0^{1}6tdt$

$v=6[\frac{t^2}{2}{]}_0^1$

$v=3m/s$

Initial velocity, $u=0m/s$

From work energy theorem,

$W=K_f-K_i$

$W=\frac{1}{2}m{v}^2-\frac{1}{2}m{u}^2$

$W=\frac{1}{2}\times 1\times 3\times 3-\frac{1}{2}\times 1\times 0\times 0$

$W=4.5-0=4.5J$

The correct option is D.