(C) Power is defined as $P = \frac{dw}{dt}$.Therefore,the work done $w$ is given by the integral of power with respect to time: $w = \int P \, dt$.Thi

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(C) Power is defined as $P = \frac{dw}{dt}$.Therefore,the work done $w$ is given by the integral of power with respect to time: $w = \int P \, dt$.This implies that the work done by the force is equal to the area under the $P-t$ graph.Since the power $P$ is always positive (as shown in the graph above the $t$-axis),the area under the curve continuously accumulates as time $t$ increases.Therefore,the work done $w$ must always increase as time progresses from $t = 0$ to $t_2$.

Class 11 Physics Work, Energy and Power Work Done by Variable Force and Force-Displacement Graph

Medium

The graph between power $(P)$ and time $(t)$ is given below. Which of the following options is correct for the work done by the force [from $t = 0$ to time $t$]?

A
First increases till $t_1$ and then decreases till $t_2$
B
First decreases till $t_1$ and then increases till $t_2$
C
Always increases
D
Always decreases

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Work, Energy and Power

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Work Done by Variable Force and Force-Displacement Graph

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The work done by a force acting on a body is as shown in the graph. The total work done in covering an initial distance of $20 \, m$ is (in $ \, J$)

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$A$ time-dependent force $F = 6t$ acts on a particle of mass $1 \ kg$. If the particle starts from rest,the work done by the force during the first $1 \ s$ will be ............... $J$.

DifficultJEE MAIN 2017

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What will be the area under the graph of variable force versus position?

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The graph between power $(P)$ and time $(t)$ is given below. Which of the following options is correct for the work done by the force [from $t = 0$ to time $t$]?

Similar Questions

The force $F$ acting on a body varies with its position $x$ as shown in the figure. At which point is the body in unstable equilibrium?

$A$ toy car of mass $5 \, kg$ moves up a ramp under the influence of a force $F$ plotted against displacement $x$ as shown in the graph. The maximum height attained is given by:

The work done by a force acting on a body is as shown in the graph. The total work done in covering an initial distance of $20 \, m$ is (in $ \, J$)

$A$ time-dependent force $F = 6t$ acts on a particle of mass $1 \ kg$. If the particle starts from rest,the work done by the force during the first $1 \ s$ will be ............... $J$.

What will be the area under the graph of variable force versus position?

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