A general definition of rate

For a physical quantity that changes linearly with time, we can take as a definition  

Whal follows is a summary of key ideas relating to the definition of rate in cases in which time is Involved. Exercise 1.1 at the end of this section provides you with an opportunity to test your understanding of rate of change. 

For time, typical units are seconds, minutes, hours, and so on. If, for example, the physical quantity was distance then typical units could be metres and the rate of change would correspond to speed measured in, say, metres per second (m s ). Since the physical quantity changes linearly with time this means that the change in any one time interval is exactly the same as that in any other equal interval. In other words a plot of physical quantity versus time will be a straight line and there is a uniform, or constant, rate of change. 

Equation 1.1 can be written in a more compact notation. If the physical quantity is represented by y, then it will change by an amount Ay during a time interval At, and we can write 

This rate of change. Ay/At, corresponds mathematically to the slope (or gradient) of the straight line and, as already stated, has a constant value. 

---