Question

Derive relation between power, force and velocity.

Answer 1

Step 1: Deriving the relationship between power, force, and velocity

Power is given as,

$P=\frac{W}{t}$ ……(i)

where, $W$ is work done and $t$ is time.

Now, work done is given as,

$W=Fd$ ……(ii)

where, $F$ is force and $d$ is displacement.

Therefore, on comparing the two equations the equation for power can be written as,

$P=\frac{Fd}{t}$

Now, we know that velocity is given as,

$v=\frac{d}{t}$

where, $d$ is displacement and $t$ is time.

Therefore, the equation for power in terms of force and velocity can be written as,

$$\begin{gathered} P=F\times \frac{d}{t} \\ P=Fv\left[\because v=\frac{d}{t}\right] \end{gathered}$$

Hence, the relationship between power, force and velocity can be represented as, $P=Fv$.