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A car drives to a town at 40 km/h and comes back at 60 km/h. Most students say the average speed is 50 km/h. It is 48 km/h, and the average velocity is zero. Questions like this are cheap marks for the examiner because they test definitions, not algebra. This post separates the two ideas, works four problems and lists the traps.
What is the difference between average speed and average velocity?
The NCERT Class 11 chapter on motion in a straight line defines average speed as the total path length divided by the time interval, and average velocity as displacement divided by time. Path length counts every metre travelled. Displacement only cares where you started and where you ended, with a direction.
NCERT also states the rule that links them: over a finite interval, average speed is greater than or equal to the magnitude of average velocity. They are equal only when the object moves in a straight line without turning back. OpenStax University Physics gives the everyday version: if a trip starts and ends at the same place, the average velocity is zero but the average speed is not.
At a single instant there is no such gap. Instantaneous speed is exactly the magnitude of instantaneous velocity, because over a tiny interval the path and the displacement become the same.
The JEE (Main) 2026 syllabus lists "average speed and instantaneous velocity" under Unit 2, Kinematics. Check the syllabus for your own exam year.
Why is the average speed of a round trip not the average of the two speeds?
Example 1. A car travels 60 km from A to B at 40 km/h and returns at 60 km/h.
Time out: 60/40 = 1.5 h. Time back: 60/60 = 1 h.
Total distance 120 km, total time 2.5 h.
Average speed = 120/2.5 = 48 km/h.
Displacement is zero, so average velocity is zero.
The car spends more time at the slower speed, so the slow leg counts more. For equal distances at speeds v₁ and v₂, the result is 2v₁v₂/(v₁ + v₂): here 2 × 40 × 60/100 = 48 km/h.
Example 2. Now the car drives for half the time at 40 km/h and half the time at 60 km/h, in a straight line. If the total time is 2t, the distance is 40t + 60t = 100t, so the average speed is 100t/2t = 50 km/h. Equal times give the simple average; equal distances do not. Read which one the question gives you.
How do you handle a curved path?
Example 3. A runner goes half a lap of a circular track of radius 50 m in 25 s. (These are sample numbers.)
Path length = πr = 3.1416 × 50 ≈ 157.1 m, so average speed ≈ 157.1/25 ≈ 6.28 m/s.
Displacement = the diameter, 2r = 100 m, so the magnitude of average velocity = 100/25 = 4 m/s, pointing across the track.
After a full lap the displacement is zero, so the average velocity is zero again while the average speed stays about 6.28 m/s, if the pace stays the same.
What if the motion is given as a formula?
Example 4. A particle moves along x with x = t² − 4t (x in metres, t in seconds). Find its average velocity and average speed from t = 0 to t = 3 s.
Positions: x(0) = 0, x(3) = 9 − 12 = −3 m. Displacement = −3 m, so average velocity = −3/3 = −1 m/s.
Check for a turning point: v = dx/dt = 2t − 4, which is zero at t = 2 s. The particle turns round inside the interval.
x(2) = 4 − 8 = −4 m. So it goes from 0 to −4 m (4 m), then back to −3 m (1 m).
Path length = 4 + 1 = 5 m, so average speed = 5/3 ≈ 1.67 m/s.
Dividing the 3 m displacement by 3 s and calling it speed is the trap. Whenever velocity changes sign in the interval, split the motion at the turning point. Our post on choosing the right equation of motion uses the same rule for a ball thrown upwards.
Why do students mix these up?
Physics education research suggests the confusion runs deeper than vocabulary. Trowbridge and McDermott (1980) interviewed university students about two objects moving at the same time and found that almost every failure to compare their velocities came from using position to judge velocity. Students who mix up "where it is" with "how fast it is going" will also mix up path length with displacement. Drawing the path, marking start and end, and labelling both quantities separately helps.
Common mistakes and how to avoid them
Taking the mean of two speeds. Valid only for equal time intervals.
Writing average speed as |average velocity|. Valid only for one-way, straight-line motion.
Missing a turning point in x(t) problems. Solve v = 0 first.
Giving average velocity without a direction or sign. It is a vector.
Unit slips. Convert minutes to hours, or km/h to m/s, before dividing.
A practice routine for this week
Day 1: Five round-trip problems with different speeds. Solve each from total distance over total time, then check with 2v₁v₂/(v₁ + v₂).
Day 2: Five x(t) problems. For each, find the turning point before anything else.
Day 3: Three curved-path problems: half lap, quarter lap, full lap. Write path length and displacement side by side.
Day 4: A mixed set of six, timed at two minutes each.
If you keep getting the set-up wrong rather than the arithmetic, the Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning rather than printing an answer, so you can see where path length and displacement part ways. For graph-based versions of these questions, read our guide to reading physics graphs.
Tonight, solve Example 1 again with 30 km/h out and 50 km/h back, and check your answer is 37.5 km/h.
