How is power related to work and time?

Power is the rate at which work is done or energy is transferred per unit time.

Power is a measure of how quickly work is done or energy is transferred. It is defined as the rate at which work is done or energy is transferred per unit time. Mathematically, power is given by the formula:

Power = Work done / Time taken

or

Power = Energy transferred / Time taken

The unit of power is the watt (W), which is defined as one joule per second (J/s). This means that a power of one watt is equivalent to doing one joule of work in one second.

The relationship between power, work and time can be seen from the formula for work:

Work = Force x Distance

If a force F is applied over a distance d, the work done is given by:

Work = F x d

If this work is done in a time t, the power is given by:

Power = Work / Time

Substituting the formula for work, we get:

Power = (F x d) / t

This shows that the power is directly proportional to the force applied and the distance over which it is applied, and inversely proportional to the time taken to do the work.

In summary, power is the rate at which work is done or energy is transferred per unit time. It is directly proportional to the force applied and the distance over which it is applied, and inversely proportional to the time taken to do the work.