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  4. The displacement x of a particle moving in one dimension under the action of a constant force is related to the time t by the equation t=√x+3, where x is in meters and t is in seconds. The work done by the force in the first 6 seconds is

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Q. The displacement $x$ of a particle moving in one dimension under the action of a constant force is related to the time $t$ by the equation $t=\sqrt{x}+3,$ where x is in meters and $t$ is in seconds. The work done by the force in the first $6$ seconds is

Work, Energy and Power

Solution:

$x=(t-3)^{2}$
$\Rightarrow v=\frac{d x}{d t}=2(t-3)$
at $t=0 ; v_{1}=-6\, m / s$
and at $t=6\, \sec,\, v_{2}=6\, m / s$
so, change in kinetic energy
$=W=\frac{1}{2} m v_{2}^{2}-\frac{1}{2} m v_{1}^{2}$
$=0$