Question

A time dependent force F = 10 t is applied on 10 kg block. Find out the work done by F in 2 seconds.

• A. 40 J
• B. 20 J
• C. 120 J
• D. 60 J

Answer 1

Answer: (B)

20 J

$10\times \frac{dv}{dt}=10t$

${\int }_0^{v}dv={\int }_0^{t}tdt$

$\Rightarrow v=\frac{t^2}{2}$ ..........(1)

$dW=\overrightarrow{F}.\overrightarrow{ds}$
$dW=10t.dx$
$dW=10t.v.dt$ .......... (2) $\because dx=vdt$

from (1) & (2)

$dW=10t.\left(\frac{t^2}{2}\right)dtdW=5t^{3}dt$

$W=\frac{5}{4}[t^4{]}_0^2=20J$