(D) Initial kinetic energy $(K_i)$ of the body is given by:$K_i = \frac{1}{2} m v^2 = \frac{1}{2} \times 25 \times (2)^2 = 50\, J$The work done agains

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(D) Initial kinetic energy $(K_i)$ of the body is given by:$K_i = \frac{1}{2} m v^2 = \frac{1}{2} \times 25 \times (2)^2 = 50\, J$The work done against the resistive force is equal to the area under the $F-x$ graph.Area = $\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4\, m \times 20\, N = 40\, J$According to the work-energy theorem,the final kinetic energy $(K_f)$ is:$K_f = K_i - W_{\text{resistive}}$$K_f = 50\, J - 40\, J = 10\, J$

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

Medium

The graph between the resistive force $F$ acting on a body and the distance $x$ covered by the body is shown in the figure. The mass of the body is $25\, kg$ and the initial velocity is $2\, m/s$. When the distance covered by the body is $4\, m$,its kinetic energy would be .............. $J$.

A
$50$
B
$40$
C
$20$
D
$10$

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Work, Energy and Power

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Work Done by Variable Force and Force-Displacement Graph

An object starts from rest and is acted upon by a variable force $F$ as shown in the figure. If $-F_0$ is the initial value of the force at $x=0$,then the position of the object where it again comes to rest will be:

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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 under the effect of a force $F = cx$ from $x = 0$ to $x = x_1$. The work done in the process is

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$A$ body covers a distance of $2\,m$ under the influence of a force $F = 15 - 4x\,N$,where $x$ is the distance covered by the particle in meters. The work done by the force is ............ $J$.

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The figure shows the frictional force versus displacement for a particle in motion. The loss of kinetic energy in travelling over $s = 0$ to $20\, m$ will be......$J$.

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The graph between the resistive force $F$ acting on a body and the distance $x$ covered by the body is shown in the figure. The mass of the body is $25\, kg$ and the initial velocity is $2\, m/s$. When the distance covered by the body is $4\, m$,its kinetic energy would be .............. $J$.

Similar Questions

An object starts from rest and is acted upon by a variable force $F$ as shown in the figure. If $-F_0$ is the initial value of the force at $x=0$,then the position of the object where it again comes to rest will be:

$A$ 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 .......... $m/s$.

$A$ particle moves under the effect of a force $F = cx$ from $x = 0$ to $x = x_1$. The work done in the process is

$A$ body covers a distance of $2\,m$ under the influence of a force $F = 15 - 4x\,N$,where $x$ is the distance covered by the particle in meters. The work done by the force is ............ $J$.

The figure shows the frictional force versus displacement for a particle in motion. The loss of kinetic energy in travelling over $s = 0$ to $20\, m$ will be......$J$.

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