(D) According to the work-energy theorem,the work done by the force on the particle is equal to the change in its kinetic energy.$W = \Delta KE = KE_{

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(D) According to the work-energy theorem,the work done by the force on the particle is equal to the change in its kinetic energy.$W = \Delta KE = KE_{final} - KE_{initial}$The work done is equal to the area under the $F-x$ graph.Area = (Area of rectangle from $x=0$ to $x=2$) + (Area of trapezoid from $x=2$ to $x=3$)Area = $(2\, m \times 2\, N) + \frac{(2\, N + 3\, N) \times (3\, m - 2\, m)}{2}$Area = $4\, J + \frac{5\, N \times 1\, m}{2} = 4\, J + 2.5\, J = 6.5\, J$Since the particle starts from rest,$KE_{initial} = 0$.Therefore,$KE_{final} = 6.5\, J$.

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

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$A$ particle moves in one dimension from rest under the influence of a force that varies with the distance traveled by the particle as shown in the figure. The kinetic energy of the particle after it has traveled $3\, m$ is ................ $J$.

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Work Done by Variable Force and Force-Displacement Graph

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$A$ force acts on a body of mass $10 \ kg$, resulting in its displacement given as $x = \left(\frac{t^3}{25}\right) \ m$, where $t$ is the time in seconds. The work done by the force in the first $2 \ s$ is (in $J$)

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Force acting on a body of mass $1 \ kg$ is related to its position $x$ as $F = x^3 - 3x \ N$. It is at rest at $x = 1$. Its velocity at $x = 3$ can be ......... $m/s$.

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$A$ position-dependent force $F = 7 - 2x + 3x^2 \, N$ acts on a small body of mass $2 \, kg$ and displaces it from $x = 0$ to $x = 5 \, m$. The work done in joules is

MediumAIPMT 1992

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$A$ particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to

MediumAIEEE 2004

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$A$ particle of mass $0.1 \, kg$ is subjected to a force which varies with distance as shown in the figure. If it starts its journey from rest at $x = 0$,its velocity at $x = 12 \, m$ is .......... $m/s$.

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$A$ particle moves in one dimension from rest under the influence of a force that varies with the distance traveled by the particle as shown in the figure. The kinetic energy of the particle after it has traveled $3\, m$ is ................ $J$.

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$A$ force acts on a body of mass $10 \ kg$, resulting in its displacement given as $x = \left(\frac{t^3}{25}\right) \ m$, where $t$ is the time in seconds. The work done by the force in the first $2 \ s$ is (in $J$)

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