(B) Given: Mass $m = 8 \ kg$,Position $x = \frac{1}{2} t^2$.Velocity $v = \frac{dx}{dt} = \frac{d}{dt}(\frac{1}{2} t^2) = t \ m/s$.At $t = 0 \ s$,velo

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(B) Given: Mass $m = 8 \ kg$,Position $x = \frac{1}{2} t^2$.Velocity $v = \frac{dx}{dt} = \frac{d}{dt}(\frac{1}{2} t^2) = t \ m/s$.At $t = 0 \ s$,velocity $v_i = 0 \ m/s$.At $t = 2 \ s$,velocity $v_f = 2 \ m/s$.According to the Work-Energy Theorem,the work done $W$ is equal to the change in kinetic energy $\Delta K$.$W = \Delta K = \frac{1}{2} m v_f^2 - \frac{1}{2} m v_i^2$.$W = \frac{1}{2} \times 8 \times (2)^2 - \frac{1}{2} \times 8 \times (0)^2$.$W = 4 \times 4 - 0 = 16 \ J$.

Class 11 Physics Work, Energy, Power and Collision Work Energy Theorem and Conservation of Mechanical Energy

Medium

An object of mass $8 \ kg$ moves under the influence of a force. The position of the object varies with time as $x = \frac{1}{2} t^2$,where $x$ is in meters and $t$ is in seconds. Find the work done by the force in the first $2 \ s$ in $J$.

A
$4$
B
$16$
C
$10$
D
$12$

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Class 11

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Work, Energy, Power and Collision

Subtopic

Work Energy Theorem and Conservation of Mechanical Energy

The displacement-time graph of a particle moving in a straight line is as shown in the figure. Select the correct alternative.

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$A$ block of mass $1\,kg$ slides on a rough horizontal surface. If the speed of the block decreases from $10\,m/s$ to $8\,m/s$,the thermal energy developed in this process is .................. $J$.

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$A$ particle is released from a height $H$. At a certain height $h$,its kinetic energy is two times its potential energy. The height $h$ and the speed $v$ of the particle at that instant are:

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$A$ force of $5\,N$,making an angle $\theta$ with the horizontal,acts on an object and displaces it by $0.4\,m$ along the horizontal direction. If the object gains a kinetic energy of $1\,J$,the horizontal component of the force is......$N$. (in $.5$)

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The potential energy of a $1 \ kg$ particle free to move along the $x-$axis is given by: $U(x) = (\frac{x^4}{4} - \frac{x^2}{2}) \ J$. The total mechanical energy of the particle is $2 \ J$. Then,the maximum speed (in $m/s$) is:

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An object of mass $8 \ kg$ moves under the influence of a force. The position of the object varies with time as $x = \frac{1}{2} t^2$,where $x$ is in meters and $t$ is in seconds. Find the work done by the force in the first $2 \ s$ in $J$.

Similar Questions

The displacement-time graph of a particle moving in a straight line is as shown in the figure. Select the correct alternative.

$A$ block of mass $1\,kg$ slides on a rough horizontal surface. If the speed of the block decreases from $10\,m/s$ to $8\,m/s$,the thermal energy developed in this process is .................. $J$.

$A$ particle is released from a height $H$. At a certain height $h$,its kinetic energy is two times its potential energy. The height $h$ and the speed $v$ of the particle at that instant are:

$A$ force of $5\,N$,making an angle $\theta$ with the horizontal,acts on an object and displaces it by $0.4\,m$ along the horizontal direction. If the object gains a kinetic energy of $1\,J$,the horizontal component of the force is......$N$. (in $.5$)

The potential energy of a $1 \ kg$ particle free to move along the $x-$axis is given by: $U(x) = (\frac{x^4}{4} - \frac{x^2}{2}) \ J$. The total mechanical energy of the particle is $2 \ J$. Then,the maximum speed (in $m/s$) is:

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