Question

Power $\left(P\right)$ versus time $\left(t\right)$ graph for a force acting on a body is given below. Then, the work done by the force upto time $t\le t_0$

• A. First decreases then increases
• B. First increases then decreases
• C. Always increases
• D. Always decreases

Answer 1

The correct option is C Always increases

Power delivered by a force is rate of work done.
$P=\frac{dW}{dt}$
$\Rightarrow W=\int Pdt$
where $W=$ work done by force
$\therefore W=\text{Area under}P\text{Vs}t\text{curve}$
$\Rightarrow$From the graph, as time $t$ increases the area under under curve keeps on increasing.

Area under the curve is summation of area of every small strip created when the curve grows.


$\Rightarrow$Area under the $(P-t)$ curve is always increasing, as area of each small strip is generated with increase in time.
$\therefore$Work done by force continuously increases.