Uniform and non-uniform motion

Stand at the roadside and watch two vehicles go by: a train gliding past on a straight, empty track, and a scooter weaving through city traffic. Both are moving, but they are moving in fundamentally different ways. The train, second after second, covers almost exactly the same distance. The scooter speeds up, brakes, swerves, and crawls — no two seconds look alike. This single distinction, equal distance in equal time versus unequal distance in equal time, is the very first classification a physicist makes about motion, and it is the doorway into everything else the Class 9 Motion chapter builds: speed, average speed, and eventually acceleration. Get comfortable telling the two apart from a table of readings or a graph, and the rest of the chapter falls into place.

The core insight

Motion is uniform if an object covers equal distances in every equal interval of time (constant speed, a straight distance-time graph), and non-uniform if the distances covered in equal time intervals are unequal (changing speed, a curved distance-time graph).

The core idea

Uniform motion. An object is in uniform motion if it covers equal distances in equal intervals of time, however small those intervals are chosen to be. Its speed does not change from moment to moment. A train holding a steady speed on a straight track, or an idealised clock hand, are the standard textbook pictures — genuinely uniform motion is rare in daily life but is the simplest case to reason about first.

Non-uniform motion. An object is in non-uniform motion if it covers unequal distances in equal intervals of time. Its speed is changing — increasing, decreasing, or both at different moments. A bus pulling away from a stop, a car in traffic, or a ball rolling to a stop under friction are all non-uniform: almost all real-world motion is.

The test, in one line. There is no separate formula to apply here — the test is a comparison. Pick a fixed interval of time (say, every 1 second, or every 2 seconds), read off the distance covered in each such interval, and compare those distances. Equal distances in equal intervals means uniform; unequal distances in equal intervals means non-uniform. The intervals being compared must be equal for the comparison to mean anything — comparing distance covered in a 1-second window against distance covered in a 3-second window tells you nothing about whether the motion is steady.

Reading it off a graph. A distance-time graph turns the same test into a shape. Uniform motion plots as a straight line — equal time steps along the horizontal axis always correspond to equal rises along the vertical axis, so the slope (which represents speed) stays constant. Non-uniform motion plots as a curve — the slope keeps changing, steeper where the object is faster and flatter where it is slower, so equal time steps correspond to unequal rises.

Figure

Two distance time graphs side by side, one a straight line for uniform motion and one a curve for non uniform motion, each with equal time steps marked showing equal or unequal rises

Why it works

There is no algebraic formula that separates uniform from non-uniform motion — the idea rests entirely on comparing distances covered in matched time slots, so it is worth seeing exactly why that comparison is the right test and where it can trip a careful student up.

Step 1. Fix what "equal intervals" means. Choose any duration — 1 second, 1 minute, whatever the data gives you — and mark off the timeline into successive slots of exactly that duration: $0$ to $1\ \text{s}$ , $1$ to $2\ \text{s}$ , $2$ to $3\ \text{s}$ , and so on. The slots must all be the same length; this is the one condition the whole test depends on.

Step 2. Read the distance covered inside each slot, not the total distance travelled so far. If a table gives you cumulative distance at each clock reading, you must first subtract successive readings to get the distance covered within each slot — comparing raw cumulative totals directly (instead of the differences) is a common source of error.

Step 3. Compare the slot-by-slot distances. If every slot shows the same distance covered, the object's speed never changed during any of those intervals, which is exactly what "uniform" means. If the slot distances differ, the object sped up or slowed down somewhere inside the interval, and the motion is non-uniform — even if just one slot breaks the pattern.

Step 4. Connect this to the graph picture. Because speed is distance divided by time, and the time slots are all equal, equal distances in each slot mean equal speed throughout — a graph of distance against time then rises by the same amount over each equal time step, which is precisely a straight line. Unequal slot distances mean the rise changes from step to step, which bends the line into a curve. The straight-line-versus-curve rule is not a separate fact to memorise; it falls directly out of the equal-interval comparison.

Worked example

Question: A cyclist's position is recorded every 2 seconds: the distances covered in the four successive 2-second intervals are $6\ \text{m}$ , $6\ \text{m}$ , $6\ \text{m}$ , $6\ \text{m}$ . A second cyclist, recorded the same way, covers $6\ \text{m}$ , $9\ \text{m}$ , $13\ \text{m}$ , $18\ \text{m}$ in the corresponding intervals. Classify each cyclist's motion, and sketch what each distance-time graph would look like.

Step 1. Check cyclist 1's interval distances: $6\ \text{m}, 6\ \text{m}, 6\ \text{m}, 6\ \text{m}$ across four equal 2-second slots. Every slot shows exactly the same distance.

Step 2. Since the time intervals are equal and the distances covered in them are equal, cyclist 1's motion is uniform. Their speed in each interval is $6\ \text{m} \div 2\ \text{s} = 3\ \text{m/s}$ , unchanging, so the distance-time graph is a straight line of constant slope $3\ \text{m/s}$ .

Step 3. Check cyclist 2's interval distances: $6\ \text{m}, 9\ \text{m}, 13\ \text{m}, 18\ \text{m}$ across the same equal 2-second slots. These are not equal to one another — the distance covered per slot keeps growing.

Step 4. Since equal time intervals produce unequal distances, cyclist 2's motion is non-uniform; the rider is speeding up throughout, going from $3\ \text{m/s}$ in the first interval to $9\ \text{m/s}$ in the last. Cyclist 1 is uniform (straight-line graph, constant $3\ \text{m/s}$ ); cyclist 2 is non-uniform (curved graph, speed rising from $3\ \text{m/s}$ to $9\ \text{m/s}$ ).

Competitive stretch

A quick sanity check worth building as a habit: for cyclist 2, the increase per interval is $9-6=3$ , $13-9=4$ , $18-13=5$ — even the increase is growing, meaning the cyclist is not just non-uniform but is speeding up at a growing rate. Spotting this pattern (a table where even the differences of differences are non-zero) is a useful early preview of what "changing acceleration" will look like once the chapter reaches that idea.

Common traps

Thinking uniform motion must mean a straight-line path — uniformity is about equal speed in equal time intervals, and has nothing to do with whether the path itself is straight or curved.
Comparing total distance and total time only, instead of checking several equal, successive intervals — a single average can hide large swings in speed along the way.
Subtracting cumulative distances incorrectly, or comparing distances from unequal-length intervals, which makes even genuinely uniform motion look non-uniform.
Assuming a straight distance-time line must pass through the origin — a straight line starting at any nonzero distance is still uniform motion, since it is the constant slope, not the starting point, that matters.

Ask the tutor: Paste your own distance-time table or graph and ask the AI tutor to walk through classifying it as uniform or non-uniform with you.

Is a car moving at constant speed around a circular track in uniform motion?

Not in the full physics sense used later in the course, but for this chapter's definition — equal distance covered in equal time — yes, its speed along the track stays constant, so it satisfies the equal-distance-in-equal-time test. What changes is its direction, not the distance it covers per second. Class 9 Motion only asks about distance and speed, so such a car counts as uniform motion here; the distinction between constant speed and constant velocity (which cares about direction too) is introduced only later.

If a table shows equal distances in every 2-second interval, could the motion still be non-uniform inside each 2-second window?

In principle yes — the object could speed up and slow down back to the same average within each 2-second slot, and a coarse table would not catch it. This is exactly why the definition says "however small the time intervals," meaning the equal-distance test should hold even as you shrink the interval. In practice, a Class 9 problem gives you the finest interval it wants you to check, and you classify based on that data; you are not expected to imagine finer sub-intervals unless the question asks.

Why do we need average speed at all if we can just check uniform or non-uniform from a table?

Classifying motion as uniform or non-uniform tells you whether the speed changed, but not a single number to describe the journey. For non-uniform motion, the speed is different at every instant, so there is no one "the speed" to quote — average speed (total distance divided by total time) gives a single useful summary figure for the whole journey, even though the object's actual speed was above and below that average at different moments. For uniform motion, the average speed and the actual speed at every instant are the same number, which is part of why uniform motion is the simpler case to start with.