Power

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

Where: P = Power (Watts) W = Work Done (Joules) t = Time (Seconds)

$P = F \cdot v$

Alternatively, for mechanical power: F = Force (Newtons) v = Velocity (m/s)

When 1 Joules of work is done per second the power produced is a watt. Watt is the unit for measuring electrical power.

Suppose that two cranes each lift objects having masses of 200kg to a height of 12m. Crane A lifts its object in 10sec while crane B requires 15sec to lift its object. Assume they lift the objects at a constant velocity they do the same amount of work.

Each did a work that was equivalent to 23520J

How much power is required to accelerate a 1000kg car from rest to 26.7m/s in 8 seconds?

The work done on the car increases its kinetic energy:

$KE = \frac{1}{2} m v^2$

Substitute the values:

$KE = \frac{1}{2} \times 1000 \, \text{kg} \times (26.7 \, \text{m/s})^2$

$KE = 356{,}445 \, \text{J}$

The power required is given by:

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

$P = \frac{356{,}445 \, \text{J}}{8 \, \text{s}} = 44{,}555.625 \, \text{W}$

Car engine is rated in horsepower (hp) where 1hp = 746watts. What is the required power measured in horsepower?

Car engines are rated in horsepower (hp), where:

$1 \, \text{hp} = 746 \, \text{W}$

Convert power to horsepower:

$\text{Power in hp} = \frac{44{,}555.625}{746}$

$\text{Power in hp} = 59.73 \, \text{hp}$

Since work causes a change in energy, power can be considered as the rate of change of energy.