1. What Is Average Speed?
Average speed tells us the overall speed of an object for the entire journey. It is useful when the speed keeps changing during the trip.
Instead of looking at speed at every moment, we look at the total distance covered and the total time taken.
1.1. Why Average Speed Is Needed
In real life, we rarely move at a constant speed. Vehicles slow down, speed up, stop at signals, and face traffic. Average speed helps us describe the full journey in one simple value.
2. Formula for Average Speed
The formula for average speed is:
\( \text{Average Speed} = \dfrac{\text{Total Distance}}{\text{Total Time}} \)
This tells us that the average speed depends on the entire distance travelled and the full time taken, not on individual changing speeds.
2.1. Example Calculation
If you travel 60 km in 2 hours, your average speed is:
\( \dfrac{60}{2} = 30 \, \text{km/h} \)
2.2. Units of Average Speed
Average speed is measured in the same units as speed, such as:
- meters per second (m/s)
- kilometers per hour (km/h)
3. Average Speed When Speeds Keep Changing
When the speed changes during different parts of the journey, we still use total distance and total time to find the average.
3.1. Example with Two Different Speeds
Suppose a person travels:
- 40 km at 20 km/h
- 60 km at 30 km/h
Total distance = 100 km
Total time = \( \dfrac{40}{20} + \dfrac{60}{30} = 2 + 2 = 4 \) h
Average speed = \( \dfrac{100}{4} = 25 \, \text{km/h} \)
3.2. Example: Going and Returning at Different Speeds
You travel 10 km to a place at 30 km/h and return 10 km at 10 km/h:
Time taken in first part = \( \dfrac{10}{30} = \dfrac{1}{3} \) h
Time taken in second part = \( \dfrac{10}{10} = 1 \) h
Total distance = 20 km
Total time = \( \dfrac{1}{3} + 1 = \dfrac{4}{3} \) h
Average speed = \( \dfrac{20}{4/3} = 15 \, \text{km/h} \)
4. Common Misconception About Average Speed
A common mistake is to think that average speed is simply the average of the different speeds. This is incorrect unless equal distances are travelled at each speed.
4.1. Why \( \dfrac{v_1 + v_2}{2} \) Does Not Work
Average speed does not depend on speeds alone. It depends on total distance and total time. If the times for each speed are different, the simple average of two speeds becomes wrong.
5. Average Speed in Daily Life
When we estimate how long a journey will take, we usually think in terms of average speed. For example, if a bus covers long distances with stops, passengers care about the average speed, not the exact speed at each moment.
5.1. Using Average Speed for Planning
If a train's average speed is 60 km/h, you can estimate that it will take about 5 hours to travel 300 km, even though its moment-to-moment speed may vary.