(D) Given: Mass $m = 2 \, kg$,position $x = \frac{t^2}{3}$.First,find the velocity $v$ by differentiating $x$ with respect to $t$: $v = \frac{dx}{dt}

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(D) Given: Mass $m = 2 \, kg$,position $x = \frac{t^2}{3}$.First,find the velocity $v$ by differentiating $x$ with respect to $t$: $v = \frac{dx}{dt} = \frac{d}{dt}(\frac{t^2}{3}) = \frac{2t}{3}$.At $t = 0 \, s$,velocity $v_i = \frac{2(0)}{3} = 0 \, m/s$.At $t = 2 \, s$,velocity $v_f = \frac{2(2)}{3} = \frac{4}{3} \, m/s$.According to the Work-Energy Theorem,the work done $W$ is equal to the change in kinetic energy $\Delta K.E. = \frac{1}{2} m v_f^2 - \frac{1}{2} m v_i^2$.$W = \frac{1}{2} \times 2 \times (\frac{4}{3})^2 - 0 = \frac{16}{9} \, J$.

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

Medium

Under the action of a force,a $2 \, kg$ body moves such that its position $x$ as a function of time $t$ is given by $x = \frac{t^2}{3}$,where $x$ is in metres and $t$ is in seconds. The work done by the force in the first two seconds is .......... $J$.

A
$1600$
B
$160$
C
$16$
D
$\frac{16}{9}$

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Work, Energy and Power

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Work Energy Theorem and Conservation of Mechanical Energy

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Under the action of a force,a $2 \, kg$ body moves such that its position $x$ as a function of time $t$ is given by $x = \frac{t^2}{3}$,where $x$ is in metres and $t$ is in seconds. The work done by the force in the first two seconds is .......... $J$.

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$A$ body of mass $m$ is travelling with a velocity $u$. When a constant retarding force $F$ is applied,it comes to rest after travelling a distance $s_{1}$. If the initial velocity is $2u$,with the same force $F$,the distance travelled before it comes to rest is $s_{2}$. Then,

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