Uniform vs Nonuniform Motion
Uniform motion is motion at constant velocity, in which an object covers equal distances in equal intervals of time along a straight line, while nonuniform motion is motion in which the velocity changes, so that the distances covered in equal times are unequal. In brief: in uniform motion the distance-time graph is a straight line and the acceleration is zero. In nonuniform motion the graph is curved, and the object has acceleration, because its speed, its direction or both are changing.
Few real objects move uniformly for long: cars speed up, slow down and turn. Uniform motion is an important ideal case, and a base for the study of acceleration. This guide defines both types of motion, shows how to tell them apart from data and graphs, compares their features in a table, works through a data example and corrects common mistakes.
What is uniform motion?
An object is in uniform motion if its velocity is constant, which means constant speed and constant direction. Then the distance covered is d = v × t. Examples: a ball rolling across a smooth floor (approximately), a ship cruising straight at a steady speed, a car on cruise control on a straight highway, and sound traveling through air of constant temperature. Strictly, the motion of an object with no net force on it is uniform (Newton’s first law).
- The distance-time graph is a straight line through the origin if the motion starts from rest at the origin, and its slope is the speed.
- The speed-time graph is a horizontal line.
- The average speed equals the instantaneous speed at all times.
What is nonuniform motion?
In nonuniform motion the velocity changes with time. This can happen by a change in speed (speeding up or slowing down), a change in direction (a car on a bend), or both. The motion has an acceleration. The simplest case is uniformly accelerated motion, where the velocity changes by equal amounts in equal times, as with a falling stone (ignoring air resistance).
- The distance-time graph is a curve.
- The speed-time graph is not a horizontal line: it is a sloping line (for constant acceleration) or a curve.
- The average speed generally differs from the instantaneous speed.
Note that motion in a circle at constant speed is nonuniform in the sense of velocity because the direction changes continuously. Its speed is constant, but its velocity is not.
Uniform and nonuniform motion compared
| Feature | Uniform motion | Nonuniform motion |
|---|---|---|
| Velocity | Constant | Changing |
| Acceleration | Zero | Not zero |
| Distances in equal times | Equal | Unequal |
| Distance-time graph | Straight line | Curve |
| Net force | Zero | Not zero |
| Example | Train at steady speed on straight track | Car braking, ball falling |
Worked example: identifying the type of motion from data
Two toy cars, A and B, are filmed, and their positions are recorded every second.
| Time (s) | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Car A | 0 | 3 | 6 | 9 | 12 |
| Car B | 0 | 1 | 4 | 9 | 16 |
- Car A, distance in each second: 3, 3, 3, 3 m. Equal distances in equal times, so the motion is uniform with speed 3 m/s.
- Car B, distance in each second: 1, 3, 5, 7 m. The distances increase, so the motion is nonuniform (speeding up).
- Average speed of B in each second: 1, 3, 5, 7 m/s. The speed increases by 2 m/s every second, so the acceleration is constant at 2 m/s2.
- Average speed of B over 4 s: 16 ÷ 4 = 4 m/s, which is neither of the speeds in any single second. At t = 3 s the cars are at the same position (9 m).
How was uniform motion understood?
Aristotle thought that a force is needed to keep an object moving at constant speed. Galileo, in the early 1600s, argued from experiments with balls on inclined planes that an object keeps moving at constant speed in a straight line if nothing acts to change it, and Newton made this the first law of motion in 1687. Galileo also showed that the distance of a body falling from rest is proportional to the square of the time, which is the pattern of car B (d = t2).
Where do the two types occur?
Uniform motion is a good approximation for cruising aircraft or conveyor belts, and it simplifies calculations. Most everyday journeys include nonuniform parts: starting, braking, turning and stopping at traffic lights. Engineers study both types to design vehicles and safety systems.
Which mistakes are common?
Mistake 1: Thinking that constant speed always means uniform motion
Uniform motion needs constant velocity, including direction. A car going around a roundabout at constant speed is not in uniform motion.
Mistake 2: Assuming that motion needs a force
Uniform motion needs no net force. A force is needed to change the velocity.
Mistake 3: Saying that nonuniform motion always means increasing speed
The speed may also decrease or change only in direction.
Mistake 4: Using d = v × t for nonuniform motion
That formula is exact only for constant speed. For changing speed, use the average speed or the equations for constant acceleration.