There are many situations where it is not sufficient to know how much work a force can do. It is also important to know the rate at which the work is being done. This quantity is known as power.

One unit of power is produced when work is done at the rate of 1 joule per second. This unit is called the watt (W).

A machine working at the rate of l joule per second has a power of 1 watt. If 1000 joules of work are done per second, the power is 1000 watts or 1 kilowatt (1 kw).

If we know the total work done in certain time, the average power can be found.

For example, a force that does 45 joules of work in 9 seconds is working at an average rate of 5 joules per second,

i.e. the average power of the force is 5 watts.

 

Power of a Moving Vehicle

The power of a vehicle is defined as

the rate at which the driving force is working.

A vehicle that has a speed of v m/s is moved v metres in 1 second by the driving force, D newtons.

Therefore the work done in 1 second by the driving force is Dv joules.

i.e. the power of the vehicle is Dv joules/second which is Dv watts.

Therefore, if H watts is the power of a vehicle,

H = Dv

If the speed of the vehicle is constant, both D and v are constant and therefore the power is constant.

If the speed is not constant, the value of Dv gives the power at the instant when the speed is v m/s.

Note that if the vehicle is stationary, its power is zero. This emphasizes the difference between the meaning of power in mechanics and the way the word is used in the motor trade.

There is a maximum value of the power a particular vehicle can generate. When the maximum power is used in a given situation, the speed produced is also maximum. In this condition no acceleration is possible so the resultant force acting on the vehicle is zero.

A vehicle can use less power than the maximum available if, for example, a lower speed is desirable or the resistance falls.