Why Your Average Speed Isn't the Average of Your Speeds

40 km/h for half the journey and 60 for the other half averages 48, not 50 — and the reason explains most of the Class 9 motion chapter. Worked out step by step,…

Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated Aug 25, 2026

Here is a question that catches out more students than almost any other in Class 9 physics, and it looks trivial:

*A car travels the first half of a journey at 40 km/h and the second half at 60 km/h. What is its average speed?*

The obvious answer is 50 km/h. The obvious answer is wrong. The correct answer is 48 km/h, and understanding why fixes a misunderstanding that runs through the whole motion chapter.

Why 50 is wrong

Average speed has a definition, and it is not "the average of the speeds":

Average speed = total distance travelled ÷ total time taken

Notice what that formula divides by. Not by the number of speeds — by time. And the car does not spend equal time at each speed. It spends far longer on the slower half.

Work it through with real numbers. Let each half be 100 km.

• First half: 100 km at 40 km/h takes 100 ÷ 40 = 2.5 hours
• Second half: 100 km at 60 km/h takes 100 ÷ 60 = 1.67 hours

Total distance is 200 km. Total time is 4.17 hours.

Average speed = 200 ÷ 4.17 = 48 km/h

The slower half consumed 2.5 of the 4.17 hours — sixty per cent of the journey time. Because it dominates the clock, it drags the average down below the midpoint. Averaging 40 and 60 directly would only be correct if the car spent equal *time* at each speed, which it does not.

The shortcut, and when it applies

For two equal distances at speeds a and b, there is a formula:

Average speed = 2ab ÷ (a + b)

Check it: (2 × 40 × 60) ÷ (40 + 60) = 4800 ÷ 100 = 48 km/h. It agrees.

This is the harmonic mean, and it is always less than or equal to the ordinary average. That is not a coincidence — it is exactly the effect of the slow section eating more time.

But read the question before reaching for it, because the other case is genuinely different. For two equal times at speeds a and b:

Average speed = (a + b) ÷ 2

If the car had driven for one hour at 40 and one hour at 60, the answer really would be 50 km/h. Same two speeds, different answer, because the weighting changed.

Equal distances → 2ab/(a+b). Equal times → (a+b)/2. Examiners set both, and they look nearly identical on the page.

Speed and velocity are not the same average

A second trap sits alongside the first. Speed uses distance; velocity uses displacement.

Consider a runner completing exactly one lap of a 400 m track in 100 seconds:

• Average speed = distance ÷ time = 400 ÷ 100 = 4 m/s
• Average velocity = displacement ÷ time = 0 ÷ 100 = 0 m/s

Her displacement is zero because she finished precisely where she started. She was moving the entire time, and her average velocity is still zero.

This has a useful consequence worth remembering: average speed can only be zero if the object never moved at all, since distance can never decrease. Average velocity is zero whenever the object returns to its starting point, however far it travelled.

Instantaneous speed versus average speed

One more distinction. When your car's speedometer reads 55 km/h, that is instantaneous speed — how fast you are going at that exact moment.

Average speed describes an entire journey and conceals everything inside it. A drive that averaged 35 km/h may have touched 80 on an open stretch and sat at 0 for twenty minutes in traffic. Both facts are invisible in the average.

The two are equal only in uniform motion, where the object covers equal distances in equal intervals of time. In all real motion they differ.

The three things to carry into the exam

1. Average speed = total distance ÷ total time. Never the average of the speeds.
2. Equal distances → 2ab/(a+b). Equal times → (a+b)/2. Check which one the question gives you.
3. Speed uses distance, velocity uses displacement. One lap of a track: speed is non-zero, velocity is zero.

Get those three right and the average-speed question stops being a trap and becomes three free marks.

For the full comparison including worked numericals, board-style questions and a diagram, see our Speed vs Average Speed page.