Power Formula

The Formula

P = \frac{W}{t} = Fv (work divided by time, or force times velocity)

When to use: How fast you use or produce energy. A powerful engine does work quickly.

Quick Example

Two people lift the same box to the same height. The faster one uses more power.

Notation

P is power in watts (W), where 1 W = 1 J/s. W is work in joules, t is time in seconds, F is force in newtons, and v is velocity in m/s.

What This Formula Means

The rate at which work is done or energy is transferred, measured in watts (joules per second).

How fast you use or produce energy. A powerful engine does work quickly.

Formal View

Power is defined as P = \frac{dW}{dt}. For a constant force, P = \vec{F} \cdot \vec{v}. Average power over an interval is \bar{P} = \frac{\Delta W}{\Delta t}.

Worked Examples

Example 1

easy
A motor does 6000 \text{ J} of work in 30 \text{ s}. What is the power output?

Solution

  1. 1
    Use the power formula: P = \frac{W}{t}.
  2. 2
    Substitute the values: P = \frac{6000}{30}.
  3. 3
    P = 200 \text{ W}

Answer

P = 200 \text{ W}
Power is the rate of doing work or transferring energy. It tells us how quickly energy is used, not just how much.

Example 2

medium
A 70 \text{ kg} person runs up a 5 \text{ m} staircase in 4 \text{ s}. What is the power output? Use g = 9.8 \text{ m/s}^2.

Common Mistakes

  • Confusing power with energy or work — power is the rate of energy transfer, not the total amount of energy transferred.
  • Forgetting to convert units — mixing kilowatts with joules or hours with seconds leads to incorrect answers.
  • Using P = Fv when the force is not constant or not in the direction of motion — the general form requires P = \vec{F} \cdot \vec{v}.

Why This Formula Matters

Power determines how quickly engines, motors, and electrical devices can deliver energy. It is the key specification for car engines, light bulbs, and power plants, and governs electricity bills and energy efficiency ratings.

Frequently Asked Questions

What is the Power formula?

The rate at which work is done or energy is transferred, measured in watts (joules per second).

How do you use the Power formula?

How fast you use or produce energy. A powerful engine does work quickly.

What do the symbols mean in the Power formula?

P is power in watts (W), where 1 W = 1 J/s. W is work in joules, t is time in seconds, F is force in newtons, and v is velocity in m/s.

Why is the Power formula important in Physics?

Power determines how quickly engines, motors, and electrical devices can deliver energy. It is the key specification for car engines, light bulbs, and power plants, and governs electricity bills and energy efficiency ratings.

What do students get wrong about Power?

A small motor can do the same work as a big motor—it just takes longer.

What should I learn before the Power formula?

Before studying the Power formula, you should understand: work, energy.

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