Average speed is not the average of the speeds
"Average speed is not the average of the speeds" is a free, interactive Class 11 Physics simulation for NEET and JEE, built on the NCERT section "Background: position, displacement and distance" in Motion in a Straight Line. A two-leg trip at v₁ and v₂: equal-distance legs give the harmonic mean, equal-time legs the arithmetic mean; a timeline bar shows why the slow leg takes longer. NEET has asked about this idea 2 times in 10 years of papers. JEE Main asked 30 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson Background: position, displacement and distance (prerequisite recap) in Motion in a Straight Line. Change the values and watch what happens.
What it shows
NCERT § Introduction
A two-leg trip at v₁ and v₂: equal-distance legs give the harmonic mean, equal-time legs the arithmetic mean; a timeline bar shows why the slow leg takes longer.
Controls
4 to try
- Sliderv₁ 10–90 km/h
- Sliderv₂ 10–90 km/h
- Toggleequal distances / equal times
- Togglereturn trip (average velocity vs average speed)
Try this
With equal distances at 30 km/h and v₂, choose v₂ so the average speed is 40 km/h (v₂ = 60 km/h).
Common mistake
Averaging the two speeds when the legs are equal distances; equating average velocity and average speed on a round trip.
In NEET
10 years of papers
Asked 2 times in 10 years of NEET.
See the past questions: Kinematics in 1D, Motion in a Straight Line (chapter)
In JEE Main
42 shifts analysed
30 questions from Motion in a Straight Line across the 42 JEE Main shifts Lumi has analysed (2017–2026).
The idea behind it
NCERT § "Introduction"
- Background recap: the ideas in this block (displacement, path length, average velocity and average speed) are prerequisites the rest of the chapter builds on, summarised here so the later sections read clearly.
- Motion along a straight line is described by one coordinate x measured from a chosen origin, with one direction taken as positive; the choice is free, but it must be kept for the whole problem.
- A body can be handled as a single point (a point object) whenever its own size is negligible next to how far it travels during the motion being studied.
- Displacement is the change in position, Δx = x₂ − x₁. It carries a sign and depends only on the start and end points.
- Path length (distance) is the total length actually covered. It is never negative and is never less than the magnitude of the displacement.
- For a round trip ending at the start point the displacement is zero even though the distance covered is not.
- Average velocity is displacement divided by the time taken, while average speed is path length divided by the time taken; the two are equal in size only if the body never reverses direction.
Questions
5 answers
- What does the "Average speed is not the average of the speeds" simulation show?
- A two-leg trip at v₁ and v₂: equal-distance legs give the harmonic mean, equal-time legs the arithmetic mean; a timeline bar shows why the slow leg takes longer.
- What mistake does the "Average speed is not the average of the speeds" simulation fix?
- A common mistake it clears up: averaging the two speeds when the legs are equal distances; equating average velocity and average speed on a round trip.
- Has NEET asked about this idea?
- Yes. NEET has asked about this idea 2 times in 10 years of papers.
- Does JEE Main ask questions from Motion in a Straight Line?
- Yes. JEE Main asked 30 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
- Is this simulation free?
- Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "Background: position, displacement and distance (prerequisite recap)" in Motion in a Straight Line (Class 11 Physics).
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