Power & Speed: P = Fv
Power & Speed: P = Fv
- When a force acts along the motion, power can be found directly from the force and instantaneous speed.
- This relation joins three earlier ideas: work, rate and velocity.
Build P = Fv in two lines
- A force acting through displacement does work .
- Divide by time and use : .
Symbols
- = power transferred by the force (W)
- = force component in the direction of motion (N)
- = speed (m s^{-1})
- At constant speed on level ground, the driving force equals the total resistive force. Either magnitude may be used as .
- If the object accelerates, the driving force is greater than the resistance. Do not replace it by the resistance alone.
- On a slope, include the component of weight along the slope when finding the force that the engine must balance.
Worked example
Constant-speed car
A car travels at 24 m s⁻¹ on level ground. The total resistive force is 1.8 kN. Find the engine's useful output power.
- Constant speed means driving force = resistance = 1800 N.
- .
Answer
Your turn9702/23/M/J/25 Q3(a)
Show that the power developed in overcoming a resistive force at speed is . (9702/23/M/J/25 Q3(a))
Show worked answer
Worked answer: , so . Since , .