What is a time rate of change?
An example, of a rate of change over time is the emptying of a
water tank by opening a valve at the bottom of the tank.
The rate of flow through the valve is dependent n the pressure
difference through the orifice(valve), controlled by the difference
in the level of the water in the tank.
As the water level drops the rate of flow drops because the
pressure difference drops. The amount of time it will take to drain
the tank completely can be calculated as a rate of change over
time.
Note: this rate of flow can be elevated by elevating the tank,
thus a valve attached to the bottom of the tank directly will have
a faster rate of change but slower rate of flow than a valve
attached some distance below the tank.