When a constant force is applied to a body moving with constant acceleration, is the power of the force constant ? If not, how would force have to vary with speed for the power to be constant ?

Let the applied force is $F$ and velocity be $v$ of the body.

As known the expression for the power , $P=\frac{W}{t}$

When $W\rightarrow$work done

$t\rightarrow$ time

So, $P=\frac{W}{t}=\frac{F\times d}{t}$   [Because work $W=F\times d$]

Or $P=F\times\frac{d}{t}$

Or $P=F\times v$   [Because velocity $v=\frac{distance}{time}=\frac{d}{t}$]

Here we see that $P\propto F$ and $P\propto v$

And $F\propto\frac{1}{v}$

As given the applied force $F$ is constant and the acceleration $a$ is constant so the velocity will vary increasingly, and we find the applied force to be inversely proportional to the velocity and  therefore to remain the power to be constant, applied force $F$ should be decreased.

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Updated on: 10-Oct-2022

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