(D) The work done $W$ by a variable force $F(x)$ is given by the integral of the force with respect to displacement:$W = \int_{x_1}^{x_2} F(x) \, dx$G

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(D) The work done $W$ by a variable force $F(x)$ is given by the integral of the force with respect to displacement:$W = \int_{x_1}^{x_2} F(x) \, dx$Given $F(x) = 3x^2 - 2x + 7$,$x_1 = 0 \text{ m}$,and $x_2 = 5 \text{ m}$.$W = \int_{0}^{5} (3x^2 - 2x + 7) \, dx$Integrating term by term:$W = [x^3 - x^2 + 7x]_{0}^{5}$Substitute the limits:$W = (5^3 - 5^2 + 7(5)) - (0^3 - 0^2 + 7(0))$$W = (125 - 25 + 35) - 0$$W = 100 + 35 = 135 \text{ J}$.Thus,the work done is $135 \text{ J}$.

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

Medium

If a position-dependent force $F(x) = (3x^2 - 2x + 7) \text{ N}$ acting on a body of mass $2 \text{ kg}$ displaces it from $x = 0 \text{ m}$ to $x = 5 \text{ m}$,then the work done by the force is: (in $J$)

AP EAMCET 2025 All AP EAMCET

A
$165$
B
$115$
C
$150$
D
$135$

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Work, Energy, Power and Collision

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Work Done by Variable Force and Force-Displacement Graph

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$A$ particle moves along the $x$-axis from $x=0$ to $x=5 \ m$ under the influence of a force $F = 7 - 2x + 3x^2$. The work done in the process is ............. (in $J$)

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Power applied to a particle varies with time as $P = (3t^2 - 2t + 1) \text{ W}$. The change in kinetic energy of the particle from $t = 2 \text{ s}$ to $t = 4 \text{ s}$ is ............... $J$.

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$A$ uniform chain of mass $M$ and length $L$ is placed on a frictionless table such that $1/3$ of its length is hanging over the edge. Find the work done to pull the hanging part back onto the table.

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The value of the force constant for the given force-displacement graph is:

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The relationship between force $F$ and displacement $x$ is shown in the figure. The work done by the object for a displacement from $x = 1 \ m$ to $x = 5 \ m$ is equal to ... $J$.

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If a position-dependent force $F(x) = (3x^2 - 2x + 7) \text{ N}$ acting on a body of mass $2 \text{ kg}$ displaces it from $x = 0 \text{ m}$ to $x = 5 \text{ m}$,then the work done by the force is: (in $J$)

Similar Questions

$A$ particle moves along the $x$-axis from $x=0$ to $x=5 \ m$ under the influence of a force $F = 7 - 2x + 3x^2$. The work done in the process is ............. (in $J$)

Power applied to a particle varies with time as $P = (3t^2 - 2t + 1) \text{ W}$. The change in kinetic energy of the particle from $t = 2 \text{ s}$ to $t = 4 \text{ s}$ is ............... $J$.

$A$ uniform chain of mass $M$ and length $L$ is placed on a frictionless table such that $1/3$ of its length is hanging over the edge. Find the work done to pull the hanging part back onto the table.

The value of the force constant for the given force-displacement graph is:

The relationship between force $F$ and displacement $x$ is shown in the figure. The work done by the object for a displacement from $x = 1 \ m$ to $x = 5 \ m$ is equal to ... $J$.

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