Mechanical power
Rate of work transfer; in force/speed mode the collinear same-direction magnitude is used.
Physics · Mechanics · Motion & Energy
Mechanical power — work/time and force/speed
Use average power P = W/Δt for work transferred over a duration, or P = Fv when the useful force and velocity are collinear and point in the same direction.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
Results
Transferred work
Work magnitude accumulated over the selected duration.
Elapsed time
Duration required at the specified nonzero power.
Relation and numerical substitution
P = W / Δt ; P = Fv—
Work/time modes use nonnegative magnitudes and a strictly positive elapsed time. Force/speed mode uses magnitudes and assumes the useful force is collinear with and points in the direction of velocity. The general instantaneous relation is P = F · v.
01Formulas and symbols
Formulas used
P
P = W / ΔtAverage power from transferred work and elapsed time.W
W = P × ΔtTransferred work from power and elapsed time.Δt
Δt = W / PElapsed time from transferred work and nonzero power.P
P = F × vMechanical power for collinear force and velocity pointing in the same direction.02Assumptions and limits
Scope of validity
- Work/time modes use nonnegative magnitudes and a strictly positive elapsed time.
- Force/speed mode uses magnitudes and assumes the useful force is collinear with and points in the direction of velocity. The general instantaneous relation is P = F · v.
03Validation example
Reference numerical case
- 600 J transferred in 3 s gives P = 200 W.
- 2 kW maintained for 30 s gives W = 60 kJ.
- A 100 N useful force at 2 m/s gives P = 200 W when force and velocity are collinear and aligned.
04References
Technical references
- University Physics Volume 1, §7.4 Power — OpenStax
FAQ
When can I use P = Fv?
Use this scalar form when F and v are magnitudes and the useful force is collinear with the velocity in the same direction. In general, instantaneous mechanical power is the dot product P = F · v.
Is power the same as energy?
No. Work or energy is measured in joules; power is the rate of energy transfer, measured in watts, where 1 W = 1 J/s.
Can power or work be zero?
Yes, zero is valid in modes where the selected equation remains defined. When solving Δt = W/P, both W and P must be greater than zero so the requested duration is strictly positive.
05Two compatible views of mechanical power
Average power divides transferred work by elapsed time: P = W/Δt. Rearranging gives W = PΔt and Δt = W/P. For instantaneous translational motion, P = F · v; the force/speed mode uses the special aligned case P = Fv.
06Magnitude and direction limits
The force/speed mode does not accept an arbitrary force direction and does not calculate a cosine factor. If force and velocity are not aligned, use the vector dot product instead. Work/time modes describe an average over the entered duration and do not reconstruct a motion history.
07Power, work and time checks
Keep joules, watts and seconds dimensionally distinct. A kilowatt is 1000 watts, while a kilojoule is 1000 joules. Do not divide by zero power when solving for time.