Rate tells us how a quantity changes with respect to time. When you see the word “per”, it usually refers to rate.
Example of rates
Speed is a rate. It measures distance travelled per unit time.
Heart rate measures the number of heart beats per unit time (usually per minute)
Flow rate measures the volume flowed per unit time.
Units of Rate
The units for rate is usually in this format: units of physical quantity/ units of time.
For example, if we are looking at the flow rate, then the units will be units of volume/ units of time. If the volume is measured in litres (l), and the time is measured in seconds (s), then the units for flow rate is l/s.
Let’s look at another example of rate — speed. If the distance is measured in kilometres (km) and the time is measured in hours (h), then the units for speed is km/h.
Instantaneous Rate vs Average Rate
Instantaneous rate is the rate at a single exact moment in time. Average rate is the overall rate across a whole period of time, found by dividing the total change by the total time taken. The difference is that average rate looks at the entire interval and smooths everything out, while instantaneous rate focuses only on one specific point or moment.
Instantaneous Rate = Change in a physical quantity at a particular point in time
Average Rate = Change in Quantity / Time Taken
On a car’s speedometer, the number you see while you are driving is your instantaneous rate — it shows how fast the car is travelling right now at this exact second. If you take a closer look, you will notice that this value on the speedometer is always fluctuating as it is measuring how fast the car is travelling at every instant. The road conditions may change (e.g. there is a red light, the car in front has slowed down, or the driver wants to overtake another car, etc.). The instantaneous speed is not a good measure of how fast or slow a car is moving because of this fluctuations. Instead, we look at the average speed to determine how fast or slow it has travelled. This can be found by taking the change in distance travelled divided by the time taken during this period.
Note that if the rate is constant, then the instantaneous rate = average rate.
Useful Formulae
Let’s assume we are looking at rate of change of A.
Average Rate of A = \( \frac{\text {change in A}}{\text{time taken}} \)
Units of rate = units of A/ units of time
(e.g. if A has units of m³ and time has units of h, then units of rate = m³/h)
Example Questions on Rate
Example 1
A tank with a capacity of 50 l was filled completely in 10 min. Find the average rate of increase of volume.
Rate = 50 l / 10 min = 5 l/min
Example 2
Flour was filled into a tank at a constant rate of 2.5 kg/min. How much flour is filled after 30 min?
Amount of flour = 2.5 kg/min x 30 min = 75 kg