Power

1. Definition of Power

• Power is the rate at which work is done or energy is transferred.
• It is a scalar quantity.
• The SI unit of power is the Watt $(W)$, where $1 W = 1 J/s.$

2. Power Formulae

a) Instantaneous Power

$P = \frac{W}{\Delta t}$

where:

• $P =$ Power $(W)$
• $W =$ Work done $(J)$
• $\Delta t =$ Time taken $(s)$

b) Average Power

$P_a = F v_{\text{avg}}$

where:

• $P_a =$ Average power $(W)$
• $F =$ Force $(N)$
• $v_{\text{avg}} =$ Average velocity $(m·s⁻¹)$

3. Work-Power Relationship

• Power depends on how fast work is done.
• Higher power output means work is done faster.
• Lower power output means work is done slower.

4. Examples of Power in Physics

a) Power in Vehicles

• A car's engine provides power to overcome forces such as friction and gravity.
• The applied force must be calculated using: $F_{\text{applied}} = F_{\text{friction}} + F_{\text{parallel}}$

where:

• $F_{\text{parallel}} =$ Component of weight acting down the slope.

b) Power in Lifting Systems

• A pump lifting water does work against gravity.
• Work done is determined using the Work-Energy Theorem.

c) Power in Mechanical Systems

• Machines perform work by applying force over time, transferring energy efficiently.

5. Key Takeaways

✔ Power is the rate at which work is done or energy is transferred.

✔ Measured in watts $(W)$, where $1 W = 1 J/s.$

✔ Higher power means work is done faster.

✔ Can be calculated using work-time or force-velocity equations.

Exam Tip

💡 Always check units when calculating power – ensure time is in seconds!