Question

If a force $F$ is applied on a body and it moves with a velocity$v$, the power will be

• A. $F\times v$
• B. $\frac{F}{v}$
• C. $\frac{F}{v^2}$
• D. $F\times v^2$

Answer 1

The correct option is A

$F\times v$

Solution:

Step 1: Given that:

Note that If a force $F$ is applied to a body and it moves with a velocity$v$.

Step 2: Formula used:

Know the formula of power$P=\frac{E}{t}$, here $P$is the power, $E$the amount of energy, and$t$ time.

The formula of the energy$E=W=F\times ∆x$, here$W$ is the work done, $F$the force, and$∆x$, displacement.

Step 3: Calculate the relation force, power, and velocity.

Know that $P=\frac{E}{t}........................\left(1\right)$

Now substitute the value of $E$in the equation (1).

Therefore,

$$\begin{gathered} P=\frac{F\times ∆x}{t} \\ P=F\times \frac{∆x}{t} \end{gathered}$$

Note that $\frac{∆x}{t}$is known as the rate of the change of the displacement with respect to time. This is known as velocity and is denoted by$v$.

Therefore $Power=Force\times velocity$

Then $P=F\times v$

Hence the correct option is (A).