Average speed tells us how fast a body covers a distance in a given time. It is a fundamental quantity of kinematics, useful both in physics problems and in everyday trip planning. In this article we explain the average speed formula, the units, and we show the calculations using a concrete example.
The average speed formula
We calculate average speed by dividing the total distance travelled by the total time of motion:
- v = s / t — speed equals distance divided by time
- s = v × t — distance equals speed times time
- t = s / v — time equals distance divided by speed
The symbol v stands for speed, s for distance, and t for time.
Units
In the SI system we express speed in metres per second (m/s), but in everyday life more often in kilometres per hour (km/h):
- Distance s — metre (m) or kilometre (km)
- Time t — second (s) or hour (h)
- Speed v — m/s or km/h
The conversion between units: to change m/s into km/h, we multiply by 3.6; to change km/h into m/s, we divide by 3.6.
Worked example
A cyclist covered a distance of s = 30 km in a time of t = 1.5 h. We calculate their average speed.
- We apply the formula v = s / t.
- We substitute: v = 30 km / 1.5 h.
- We calculate: v = 20 km/h.
- In SI units: v = 20 / 3.6 ≈ 5.56 m/s.
The cyclist travelled at an average speed of 20 km/h, that is about 5.56 m/s.
Average speed versus instantaneous speed
Average speed refers to the whole route, not a single moment. If the cyclist went faster on the descents and slower uphill, the instantaneous speed changed, but the average speed averages out the entire trip. This is an important distinction in physics problems.
Calculating time or distance
The formula can be rearranged to find time or distance. To cover 90 km at a speed of 60 km/h, we need: t = s / v = 90 / 60 = 1.5 h. In turn, travelling at 80 km/h for 2 h, we will cover: s = v × t = 80 × 2 = 160 km.
Speed in everyday life
Average speed is useful not only in physics problems but also when planning a journey. Knowing the distance to your destination and the expected speed, you can easily estimate the travel time. On a city route the average speed of a car is often low because of lights and traffic jams, which is why the real travel time is longer than the maximum speed would suggest. Similarly, a pedestrian walks at an average of about 5 km/h, a cyclist at 15-20 km/h, and a long-distance train at 100-120 km/h. These rough values help you plan your day quickly.
Why don't we average the speeds directly?
A common trap: if we travelled half the route at 60 km/h and the other half at 40 km/h, the average speed is not 50 km/h. You have to work out the total distance and the total time, and only then divide them. For two equal 60 km sections the time is 1 h and 1.5 h respectively, so the average is 120 km / 2.5 h = 48 km/h, not 50 km/h.
Example with unit conversion
A train covered s = 180 km in a time of t = 2 h. We calculate the speed in km/h and m/s.
- Speed: v = s / t = 180 / 2 = 90 km/h.
- In SI units: v = 90 / 3.6 = 25 m/s.
The train travelled at an average speed of 90 km/h, that is 25 m/s.
Most common mistakes
- Inconsistent units — kilometres with seconds give a wrong result. Reduce the data to a single system.
- Time in minutes instead of hours — 90 minutes is 1.5 hours, not 90.
- Confusing average speed with the arithmetic mean of the speeds — what counts is the ratio of the whole distance to the whole time.
- Wrong unit conversion — remember to divide or multiply by 3.6.
Frequently asked questions
- How do I change km/h into m/s? You divide the value by 3.6. For example, 72 km/h is 20 m/s.
- How does velocity differ from speed? Velocity is a vector (it has a direction), while speed is its numerical value.
- What is instantaneous speed? It is the speed at a given moment, for example a reading from a speedometer, as opposed to the average over the whole route.
Summary
Average speed v = s / t is the ratio of the total distance to the total time. We express it in m/s or km/h, remembering the conversion factor of 3.6. Knowing two of the three quantities, you can easily find the third.
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