Average Speed: Formula, Rules and Solved Questions
Average Speed is the total distance travelled divided by the total time taken. It is not usually the arithmetic mean of individual speeds. For equal distances, use the harmonic-mean formula, while for equal time intervals, use the arithmetic mean. This page covers formulas, unit conversions, shortcuts, and solved calculation methods.
What Is Average Speed?
Time must include the complete journey, including stops or waiting periods when the question treats them as part of the journey. For example, if a vehicle covers 120 km in 3 hours, its average speed is 120 ÷ 3 = 40 km/h.
Average Speed Formula & Tricks
Important Formulas
Use the complete distance and the complete time for the journey.
If equal distances are covered at speeds u and v, the average speed is the harmonic mean of the two speeds.
If the object travels at speeds u and v for equal amounts of time, the average speed is their arithmetic mean.
Add all distances and divide by the sum of all corresponding times.
Multiply by 18/5 to convert m/s to km/h and by 5/18 to convert km/h to m/s.
Quick Tricks
For two equal-distance parts, do not take the ordinary average of the speeds. Directly use 2uv/(u+v).
When the time spent at each speed is equal, average speed equals the arithmetic mean of the speeds.
Convert all speeds, distances, and times to compatible units before applying the formula.
Average Speed Concepts
Total distance and total time method
Calculate the distance covered in each part, add the distances, add the times, and then divide. If a vehicle covers 150 km in 3 hours and 100 km in 2 hours, total distance = 250 km and total time = 5 hours, so average speed = 50 km/h.
Average speed for equal distances
Suppose each distance is d. Total distance is 2d, while total time is d/u + d/v. Therefore, average speed = 2d ÷ (d/u + d/v) = 2uv/(u+v). This value is less than the ordinary arithmetic mean when u and v are different.
Average speed for equal time intervals
If the time at each speed is t, the total distance is ut + vt and total time is 2t. Hence, average speed = (ut + vt)/(2t) = (u+v)/2.
Effect of stoppage or rest
If a vehicle covers distance D in travelling time T and stops for R hours, average speed including the stop is D/(T+R). If the question asks for running speed, use only the travelling time.
Unit conversion in speed calculations
To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5. Distance in kilometres divided by time in hours gives km/h, while distance in metres divided by time in seconds gives m/s.
Average Speed Video Lessons
Watch short topic-wise lessons for quick revision.
Average Speed and the Harmonic Mean Trap
Understand why average speed for equal distances uses the harmonic mean, and learn to avoid the common mistake of taking the simple arithmetic average of speeds.
Practice Average Speed Questions
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Average Speed Quick Quiz
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Average Speed Revision Points
Use these formulas and rules for quick calculation.
- Average Speed = Total Distance ÷ Total Time.
- For equal distances at u and v, average speed = 2uv/(u+v).
- For equal time intervals at u and v, average speed = (u+v)/2.
- Average speed is not generally the arithmetic mean of individual speeds.
- Include stoppage time when the question asks for average speed for the complete journey.
- 1 m/s = 18/5 km/h and 1 km/h = 5/18 m/s.
- Use the same units for all distances and times before applying a formula.
Average Speed FAQs
What is the average speed formula?
Average Speed = Total Distance ÷ Total Time. Use the complete distance and total time of the journey.
What is the average speed for equal distances at 40 km/h and 60 km/h?
Average speed = 2 × 40 × 60 ÷ (40 + 60) = 48 km/h.
When can the arithmetic mean of two speeds be used?
Use (u+v)/2 when the object travels at the two speeds for equal time intervals, not merely for equal distances.
A car travels 180 km in 3 hours and stops for 1 hour. What is its average speed including the stop?
Total time is 4 hours, so average speed = 180 ÷ 4 = 45 km/h.
How do you convert 54 km/h into m/s?
Multiply by 5/18: 54 × 5/18 = 15 m/s.
Can average speed be greater than the highest speed in a journey?
No. For positive distances and times, average speed lies between the lowest and highest speeds used.