BitWithBite
Mechanics · Quick Reference
Power Cheat Sheet
In one line: power measures how quickly work gets done or energy gets transferred — the same amount of work can be done slowly with little power, or quickly with a lot.
Key Ideas
1Power Definition. The rate at which work is done or energy is transferred: P = W/t, where W is work and t is time.
2Units of Power. Measured in watts (W), where 1 watt = 1 joule per second.
3Power and Velocity. For a constant force, power can also be written as P = F*v, where v is the object's velocity in the direction of the force.
4Average vs. Instantaneous Power. Average power is total work divided by total time; instantaneous power is the power at one specific moment, which may vary if force or velocity changes.
5Efficiency. The ratio of useful power output to total power input, often expressed as a percentage; no real machine is 100% efficient due to losses like friction and heat.
Worked Examples
A motor does 500 J of work in 10 seconds. Find its power output.
50 W
A car engine exerts 2000 N of force while moving at 15 m/s. Find the power output.
30,000 W (or 30 kW)
A machine has power input 1000 W and useful power output 750 W. Find its efficiency.
75%
Formulas
P = W/t
P = F*v
Practice Yourself
A machine does 1000 J of work in 20s. Find power.
50 W
A force of 500 N moves an object at 4 m/s. Find power.
2000 W
A machine has input 500 W and output 400 W. Find efficiency.
80%