Power is a central concept in physics, representing the rate of work done or energy transfer. Understanding power helps explain how systems evolve under various forces.

## Power: Definition and Formula

- Power measures the rate of work or energy use per time. It's calculated as: $P = \frac{W}{t}$

## Power in Relation to Force and Velocity

- Power is also calculated by multiplying force $F$ by velocity $v$: $P = F \times v$

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## Calculating Power

- Rate of work: $P = \frac{W}{t}$
- Using force and velocity: $P = F \times v$

## Examples of Power Calculation

### Example 1: Lifting a Weight

**Scenario:** Lifting a 20 kg weight to a height of 2 meters in 4 seconds. Calculate the force, work done, and power.

**Solution:**

**1. Force due to Gravity:**

- $F = mg = 20 \times 9.8 = 196 \, \text{N}$

**2. Work Done:**

- $W = F \times h = 196 \times 2 = 392 \, \text{J}$

**3. Power:**

- $P = \frac{W}{t} = \frac{392}{4} = 98 \, \text{Watts}$

**4. Conclusion:** The power required to lift the weight is 98 Watts.

### Example 2: **Car Moving at Constant Velocity**

**Scenario:** Calculate the power for a car moving at 25 m/s under a force of 500 N.

**Solution:**

**1. Calculating Power:**

- Power formula for constant velocity: $P = F \times v$
- Where $F = 500 \, \text{N}) and (v = 25 \, \text{m/s}$

- Calculation: $P = 500 \times 25 = 12500 \, \text{Watts}$

**2. Conclusion:** A car moving at 25 m/s under a force of 500 N exerts 12500 Watts of power.

Rahil spent ten years working as private tutor, teaching students for GCSEs, A-Levels, and university admissions. During his PhD he published papers on modelling infectious disease epidemics and was a tutor to undergraduate and masters students for mathematics courses.