P = Fv: power from force and speed

5 minAS Level5.1.7

AI-drafted, independently checked · not yet teacher-reviewed

By the end of this lesson

By the end you can derive and use $P = Fv$ : the power developed by a force equals the force multiplied by the speed, when the force acts along the motion.

A second way to write the same physics

Lifting a load is easy to think about: force × distance, then divide by time. A car cruising along a motorway is harder — you are not told the distance, only how fast it goes.

For something moving at a constant speed, distance and time are linked by $s = vt$ . Put that into the power equation and the time disappears.

Definition

Power in terms of force and velocity

For a force $F$ acting along the direction of motion of an object moving at constant speed $v$ :

$P = Fv$

$F$ in newtons (N), $v$ in metres per second ( $\text{m s}^{-1}$ ), $P$ in watts (W).
Check the units: $\text{N} \times \text{m s}^{-1} = \text{N m s}^{-1} = \text{J s}^{-1} = \text{W}$ ✓

Where it comes from (three lines)

Start from the definition and substitute:

$P = \dfrac{W}{t} \qquad W = Fs \qquad s = vt$

So, for a constant force acting along the motion,

$P = \dfrac{Fs}{t} = F \times \dfrac{s}{t} = Fv$

Nothing new is being invented: $P = Fv$ is just $P = \dfrac{W}{t}$ with the work done per second written in terms of speed.

Worked example: Worked example: a car cruising

A car travels at a constant speed of $30\ \text{m s}^{-1}$ . The resistive forces (drag and friction) total $400\ \text{N}$ .

What power must the engine develop?

Have a go first?

Quick check

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