1. Tardigrade
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  4. Assertion Force applied on a block moving in one-dimension is producing a constant power, then the motion should be uniformly accelerated. Reason This constant power multiplied with time is equal to the change in kinetic energy.

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Q. Assertion Force applied on a block moving in one-dimension is producing a constant power, then the motion should be uniformly accelerated.
Reason This constant power multiplied with time is equal to the change in kinetic energy.

Work, Energy and Power

Solution:

From work-energy theorem,
$W=\Delta KE =\frac{1}{2} m v^{2}$ ...(i)
The power, $P=\frac{\text { work done }}{\text { Time }}=\frac{W}{t}$
$\Rightarrow W=P \times t$ ...(ii)
From Eqs (i) and (ii), we get
$P \times t=\Delta KE =\frac{1}{2} m v^{2}$ ...(iii)
$\therefore$ Power multiplied with time is equal to the change in kinetic energy.
Also, $P=F \cdot v$
From Eq. (iii),
$v^{2} \propto t$ or $v \propto t^{1 / 2}$
Differentiating Eq. (iv), we get
$\frac{d v}{d t} \propto t^{-1 / 2}$
or $a \propto t^{-1 / 2}$
Thus, the motion is not uniformly accelerating. Therefore, Assertion is incorrect but Reason is correct.