(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, Power and Collision 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, Power and Collision

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Work Done by Variable Force and Force-Displacement Graph

$A$ body of mass $8\,kg$ is moved by a force $F = 3x\,N$,where $x$ is the distance covered. The initial position is $x = 2\,m$ and the final position is $x = 10\,m$. The initial speed is $0.0\,m/s$. The final speed is ........... $m/s$.

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$A$ particle is projected with velocity $v_{0}$ along the $x-$axis. $A$ damping force is acting on the particle which is proportional to the square of the distance from the origin,i.e.,$ma = -\alpha x^{2}$. The distance at which the particle stops is:

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What does the area enclosed by the $F-x$ graph represent? (where $F$ is the external force and $x$ is the change in the length of the spring)

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$A$ body moves from $x = 0$ to $x = x_1$ under the influence of a force $F = cx$. The work done during this process is:

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$A$ force $F = 20 + 10y$ acts on a particle in the $y$ direction,where $F$ is in newton $(N)$ and $y$ is in meter $(m)$. The work done by this force to move the particle from $y = 0$ to $y = 1 \; m$ is ...... $J$.

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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 $t$]?

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$A$ body of mass $8\,kg$ is moved by a force $F = 3x\,N$,where $x$ is the distance covered. The initial position is $x = 2\,m$ and the final position is $x = 10\,m$. The initial speed is $0.0\,m/s$. The final speed is ........... $m/s$.

$A$ particle is projected with velocity $v_{0}$ along the $x-$axis. $A$ damping force is acting on the particle which is proportional to the square of the distance from the origin,i.e.,$ma = -\alpha x^{2}$. The distance at which the particle stops is:

What does the area enclosed by the $F-x$ graph represent? (where $F$ is the external force and $x$ is the change in the length of the spring)

$A$ body moves from $x = 0$ to $x = x_1$ under the influence of a force $F = cx$. The work done during this process is:

$A$ force $F = 20 + 10y$ acts on a particle in the $y$ direction,where $F$ is in newton $(N)$ and $y$ is in meter $(m)$. The work done by this force to move the particle from $y = 0$ to $y = 1 \; m$ is ...... $J$.

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