The Concept of Average Speed
In kinematics, average speed is one of the most fundamental measurements of motion. While your car's speedometer tells you your instantaneous speed at one exact microsecond, your average speed gives you the broader picture of your entire journey.
Average speed is defined as the total distance traveled divided by the total time it took to cover that distance. Because it deals with distance (a scalar quantity) rather than displacement (a vector quantity), average speed does not care about the direction you traveled—it only cares about how much ground you covered.
Why Average Speed is Not the Mean
A common mathematical mistake when calculating average speed is attempting to take the arithmetic mean of multiple different speeds.
The Trap: If you drive to a city at $60 , \text{mph}$ and drive back home at $40 , \text{mph}$, your average speed for the entire trip is not $50 , \text{mph}$. Why? Because you spent significantly more time driving at $40 , \text{mph}$ than you did at $60 , \text{mph}$. The total time metric inherently weights the slower speed heavier.
To find the true average speed, you must always fall back to the fundamental formula: total distance divided by total time.
The Formula
Example Calculation
Let's solve the trap scenario above. Imagine the city is exactly $120 , \text{miles}$ away.
- Trip There: You drive $120 , \text{miles}$ at $60 , \text{mph}$. This takes exactly $2 , \text{hours}$.
- Trip Back: You drive $120 , \text{miles}$ back at $40 , \text{mph}$. This takes exactly $3 , \text{hours}$.
To find the true average speed:
- Total Distance: $120 , \text{miles} + 120 , \text{miles} = \mathbf{240 , \text{miles}}$.
- Total Time: $2 , \text{hours} + 3 , \text{hours} = \mathbf{5 , \text{hours}}$.
- Average Speed: $\frac{240}{5} = \mathbf{48 , \text{mph}}$.
The true average speed is $48 , \text{mph}$, not $50 , \text{mph}$.