Question

A particle of mass $1kg$ starts from rest under a time dependent force $F=1+2t$. The work done by the force in time interval $t=0$ to $t=2s$ is

• A. $18J$
• B. $20J$
• C. $30J$
• D. $\frac{70}{3}J$

Answer 1

The correct option is A $18J$

$W=\int Fds$

Now, $a=\frac{F}{m}=1+2t$

$\therefore \frac{dv}{dt}=1+2t$

${\int }_0^{v}dv={\int }_0^t(1+2t)dt$

$v=t+t^2$

Now, $W={\int }_0^{2}F\left(\frac{ds}{dt}\right)dt$

$={\int }_0^2(1+2t)\left(v\right)dt$

$={\int }_0^2(1+2t)(t+t^2)dt=18J$