(D) Initial kinetic energy $K_i = \frac{1}{2} mv^2 = \frac{1}{2} \times 2 \times (10)^2 = 100 \ J$. Work done by the resistive force is equal to the a

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(D) Initial kinetic energy $K_i = \frac{1}{2} mv^2 = \frac{1}{2} \times 2 \times (10)^2 = 100 \ J$. Work done by the resistive force is equal to the area under the $F-x$ graph. Work done $W = \text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \times 20 = 40 \ J$. Since the force is resistive,the work done is negative: $W = -40 \ J$. According to the work-energy theorem,$K_f - K_i = W$. $K_f = K_i + W = 100 - 40 = 60 \ J$.

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

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The graph of the resistive force acting on an object versus the distance covered by it is shown in the figure. The mass of the object is $2 \ kg$ and its initial velocity is $10 \ m/s$. When the distance covered by the object is $4 \ m$,its kinetic energy will be $.... \ J$. (in $J$)

A
$50$
B
$40$
C
$20$
D
$60$

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Work, Energy, Power and Collision

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Work Done by Variable Force and Force-Displacement Graph

Power applied to a particle varies with time as $P = (4t^3 - 5t + 2) \, W$,where $t$ is in seconds. Find the change in its $K.E.$ between time $t = 2 \, s$ and $t = 4 \, s$. ............... $J$

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The displacement $s$ of a body of mass $3 \,kg$ under the action of a force is given by $s = \frac{t^3}{3}$, where $s$ is in metres and $t$ is in seconds. The work done by the force in the first two seconds is (in $\,J$)

MediumTS EAMCET 2023

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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 $J$)

DifficultTS EAMCET 2020

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$A$ particle is moved along a path $A-B-C-D-E-F-A$,as shown in the figure,in the presence of a force $\vec{F} = (\alpha y \hat{i} + 2 \alpha x \hat{j}) \ N$,where $x$ and $y$ are in meters and $\alpha = -1 \ N/m$. The work done on the particle by this force $\vec{F}$ will be . . . . . . Joule.

IIT 2019

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An object of mass $500 \; g$, initially at rest, is acted upon by a variable force whose $X$-component varies with $X$ as shown in the graph. The velocities of the object at $X = 8 \; m$ and $X = 12 \; m$ are, respectively:

MediumNEET 2019

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The graph of the resistive force acting on an object versus the distance covered by it is shown in the figure. The mass of the object is $2 \ kg$ and its initial velocity is $10 \ m/s$. When the distance covered by the object is $4 \ m$,its kinetic energy will be $.... \ J$. (in $J$)

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Power applied to a particle varies with time as $P = (4t^3 - 5t + 2) \, W$,where $t$ is in seconds. Find the change in its $K.E.$ between time $t = 2 \, s$ and $t = 4 \, s$. ............... $J$

The displacement $s$ of a body of mass $3 \,kg$ under the action of a force is given by $s = \frac{t^3}{3}$, where $s$ is in metres and $t$ is in seconds. The work done by the force in the first two seconds is (in $\,J$)

$A$ 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 $J$)

$A$ particle is moved along a path $A-B-C-D-E-F-A$,as shown in the figure,in the presence of a force $\vec{F} = (\alpha y \hat{i} + 2 \alpha x \hat{j}) \ N$,where $x$ and $y$ are in meters and $\alpha = -1 \ N/m$. The work done on the particle by this force $\vec{F}$ will be . . . . . . Joule.

An object of mass $500 \; g$, initially at rest, is acted upon by a variable force whose $X$-component varies with $X$ as shown in the graph. The velocities of the object at $X = 8 \; m$ and $X = 12 \; m$ are, respectively:

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