Power
Work, Energy & Power - OCR A-Level Physics
Key Definition
Power
The rate of doing work, or the rate of energy transfer. SI unit: watt (W), where 1 W = 1 $J s^{-1}$.
The rate of doing work, or the rate of energy transfer. SI unit: watt (W), where 1 W = 1 $J s^{-1}$.
$$\begin{aligned}
P &= IV \\
&= \(I^{2}\)R \\
&= \frac{\(V^{2}\)}{R}
\end{aligned}$$
$$P = \frac{W}{t}$$
$$P = Fv$$
- $P = Fv$ is derived from $P = W/t = Fs/t = Fv (since s/t = v$ for constant velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.)
- At constant velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹., the driving force equals the resistive force (Newton's first lawAn object remains at rest or moves with constant velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹. unless acted on by a resultant force.). So $P_{engine} =$ $F_{resistanceThe opposition to currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). flow. The ratio of potential difference to currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A).. Measured in ohms (Ω).} \times$ v
- At maximum speed: all engine powerThe rate of energy transfer. Measured in watts (W). goes to overcoming drag. $P_{engine} =$ $F_{resistanceThe opposition to currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). flow. The ratio of potential difference to current. Measured in ohms (Ω).} \times$ $v_{max}$
- If a car's powerThe rate of energy transfer. Measured in watts (W). is fixed, increasing speed means the driving force must decrease
Worked Example [3 marks]
A car has a maximum powerThe rate of energy transfer. Measured in watts (W). output of 45 kW and experiences a total resistive force of 1500 N at high speeds. Calculate the maximum speed of the car.
Show Solution
1
$At maximum speed, driving force = resistive force = 1500 \text{ N} (constant velocity)$
[1]2
$P = Fv, so v = \frac{P}{F} = \frac{45000}{1500}$
[1]3
$v = 30 \text{ m s}^{-1}$
[1]Answer
$30 $m \(s^{-1}\)$$