Every object in motion tells a story — does it keep a steady pace or keep changing? Understanding this distinction is the first step to reading position-time and velocity-time graphs with confidence. From NCERT Chapter 4 (Exploration edition) Class 9 Science. Aligned with CBSE syllabus 2026-27.
Q. What is uniform motion? Give the NCERT definition.
An object is said to be in uniform motion when it covers equal distances in equal intervals of time, no matter how small those intervals are. The key word is equal — the spacing never changes.
Q. What are the key characteristics of uniform motion?
Q. Give five real-life examples of uniform (or approximately uniform) motion.
| Object | Why it approximates uniform motion |
|---|---|
| Light from a torch in a vacuum | Constant speed 3 × 10⁸ m s⁻¹, no medium to slow it |
| An express train on a straight, level track | Cruise-control keeps speed nearly constant over long stretches |
| Earth's revolution around the Sun (approx.) | Nearly circular orbit at ~30 km s⁻¹ — treated as uniform in early chapters |
| A conveyor belt at constant speed | Motor maintains fixed belt speed |
| A swimmer doing laps at a constant pace | Equal lengths covered in each equal time interval |
Q. Why is perfectly uniform motion rarely found in everyday life?
In practice, friction, air resistance, road irregularities, and human or mechanical variability always cause small fluctuations in speed. Uniform motion is an idealised model that is useful when these fluctuations are small enough to be ignored.
Q. What is non-uniform motion?
An object is in non-uniform motion when it covers unequal distances in equal intervals of time. The spacing between successive positions changes — the object is either speeding up, slowing down, changing direction, or doing a combination of these.
Q. What are the sub-types of non-uniform motion?
| Sub-type | What changes | Acceleration | Example |
|---|---|---|---|
| Uniformly accelerated | Speed (in a straight line) | Constant, non-zero | Stone in free fall |
| Non-uniformly accelerated | Speed and/or direction | Changing (variable) | Car in city traffic |
| Uniform circular motion | Direction only | Constant magnitude, changing direction | Satellite in circular orbit |
| Retardation (deceleration) | Speed decreases | Constant negative | Braking car |
Q. Give five common examples of non-uniform motion from daily life.
Q. How do you identify uniform and non-uniform motion from a position-time graph?
| p-t Graph Shape | What the slope tells us | Motion type |
|---|---|---|
| Horizontal straight line | Slope = 0 → velocity = 0 | Object at rest |
| Straight line with positive slope | Constant positive velocity | Uniform motion (forward) |
| Straight line with negative slope | Constant negative velocity | Uniform motion (backward) |
| Upward-curving parabola | Increasing slope → increasing velocity | Non-uniform, speeding up |
| Downward-curving line | Decreasing slope → decreasing velocity | Non-uniform, slowing down |
Q. How do you identify motion type from a velocity-time graph?
| v-t Graph Shape | Slope (= acceleration) | Motion type |
|---|---|---|
| Horizontal line at v = 0 | Zero | At rest |
| Horizontal line at v = constant | Zero | Uniform motion |
| Straight line, positive slope | Constant positive | Uniform acceleration (speeding up) |
| Straight line, negative slope | Constant negative | Uniform retardation (slowing down) |
| Curved line | Variable | Non-uniform acceleration |
Q. Compare uniform motion and non-uniform motion across all important parameters.
| Parameter | Uniform Motion | Non-Uniform Motion |
|---|---|---|
| Definition | Equal distances in equal intervals of time | Unequal distances in equal intervals of time |
| Speed | Constant throughout | Changes (increases, decreases, or varies) |
| Acceleration | Zero (a = 0) | Non-zero (a ≠ 0); may be constant or variable |
| Distance in successive equal Δt | Same in each interval | Different in each interval |
| Position-time graph | Straight line (non-zero slope) | Curved line (parabola or other curve) |
| Velocity-time graph | Horizontal straight line | Straight line with slope (uniform a) or curved (variable a) |
| Equations of motion | Only s = vt applies (a = 0, so u = v = constant) | Kinematic equations (v = u + at, s = ut + ½at², v² = u² + 2as) if a is constant |
| Everyday examples | Light travelling in vacuum; train at cruise speed | Car in city traffic; stone in free fall; ball thrown upward |
Q. What is uniformly accelerated motion and why is it a special case of non-uniform motion?
Uniformly accelerated motion is a sub-type of non-uniform motion in which the acceleration is constant — it neither increases nor decreases. Because the object's speed changes at a steady rate, the distances covered in successive equal time intervals are unequal (increasing if speeding up, decreasing if slowing down). This makes it non-uniform, but the regularity of the acceleration makes it mathematically tractable through the three kinematic equations.
Q. How do you recognise uniformly accelerated motion from a velocity-time graph?
A straight line with a non-zero slope on the v-t graph is the signature of uniformly accelerated motion. The slope of that line equals the constant acceleration $a$. If the line slopes upward, the object is speeding up; if it slopes downward (retardation), the object is slowing down.
Q. How are uniform motion and uniformly accelerated motion different from each other?
| Feature | Uniform Motion | Uniformly Accelerated Motion |
|---|---|---|
| Acceleration | Zero | Constant, non-zero |
| Speed | Constant | Changes uniformly |
| p-t graph | Straight line | Parabola |
| v-t graph | Horizontal line | Straight line with slope |
| Equation used | s = vt only | All three kinematic equations |
NCERT Table 4.3 gives the position of an object (a car) at different times during uniform motion along a straight road:
| Time t (s) | Position s (m) | Distance in previous 2 s (m) |
|---|---|---|
| 0 | 0 | — |
| 2 | 40 | 40 |
| 4 | 80 | 40 |
| 6 | 120 | 40 |
| 8 | 160 | 40 |
Analysis: The car covers 40 m in every 2-second interval. The distance is identical in each interval → the motion is uniform. The speed is $v = 40\,\text{m} / 2\,\text{s} = 20\,\text{m s}^{-1}$ throughout. The position-time graph of this data is a straight line passing through the origin with slope 20 m s⁻¹.
NCERT Table 4.5 gives velocity data for an object undergoing uniformly accelerated motion (from Fig. 4.17b of the textbook):
| Time t (s) | Velocity v (m s⁻¹) | Change in v in 2 s (m s⁻¹) |
|---|---|---|
| 0 | 0 | — |
| 2 | 1 | 1 |
| 4 | 2 | 1 |
| 6 | 3 | 1 |
| 8 | 4 | 1 |
Analysis: Velocity increases by 1 m s⁻¹ in every 2 seconds. The change is identical each interval, confirming constant acceleration.
$$a = \frac{\Delta v}{\Delta t} = \frac{1\,\text{m s}^{-1}}{2\,\text{s}} = 0.5\,\text{m s}^{-2}$$The position-time graph of this data is a parabola (non-uniform motion). The velocity-time graph is a straight line with slope $0.5\,\text{m s}^{-2}$ (uniformly accelerated). The three kinematic equations apply.
Problem: A cyclist records the following distances in successive 5-second intervals: 50 m, 60 m, 70 m, 80 m. Is the motion uniform, uniformly accelerated, or something else?
Check for uniform motion: Distances are 50, 60, 70, 80 m — they are not equal. So the motion is not uniform.
Check for uniform acceleration: The increase in distance per interval = 60 − 50 = 10 m; 70 − 60 = 10 m; 80 − 70 = 10 m. The increase is constant. This is the hallmark of uniformly accelerated motion.
Using the equation for distance in the $n$-th interval: $s_n = u + \frac{a}{2}(2n - 1)$, one can calculate the initial velocity $u$ and acceleration $a$ — but even without this, the equal increment in successive distances confirms uniformly accelerated motion.
Answer: The motion is uniformly accelerated (non-uniform, but with constant acceleration).
Q1. Define uniform motion. How is it different from non-uniform motion?
Q2. A car travels at 60 km h⁻¹ for 2 hours on a straight highway. Is this uniform motion? Justify your answer.
Q3. A feather falls from the top of a building. Is its motion uniform or non-uniform? What about a stone dropped from the same height in vacuum?
Q4. An object's velocity-time graph is a straight line passing through the origin with a positive slope. What type of motion does this represent? What does the slope tell you?
Q5. An object's position-time data is: t = 0, 1, 2, 3, 4 s; s = 0, 5, 20, 45, 80 m. (a) Is the motion uniform or non-uniform? (b) How can you tell from the data alone?
Distances in successive 1-s intervals: 5 − 0 = 5 m; 20 − 5 = 15 m; 45 − 20 = 25 m; 80 − 45 = 35 m.
(a) The distances are not equal (5, 15, 25, 35 m) → non-uniform motion.
(b) The increase in successive distances is constant: 15 − 5 = 10, 25 − 15 = 10, 35 − 25 = 10 m. This equal increment in distance per interval is the signature of uniformly accelerated motion. If you plotted a p-t graph it would be a parabola; the v-t graph would be a straight line.
Q6. Sketch (describe in words) the velocity-time graphs for: (a) a car moving at constant 20 m s⁻¹, (b) a train braking uniformly from 30 m s⁻¹ to rest in 10 s, (c) a ball thrown upward and catching it again at the same height.
(a) Car at 20 m s⁻¹: A horizontal line at v = 20 m s⁻¹ from t = 0 to the end. Slope = 0 → uniform motion.
(b) Train braking: A straight line with negative slope starting at v = 30 m s⁻¹ at t = 0 and reaching v = 0 at t = 10 s. Slope = (0 − 30)/10 = −3 m s⁻² (retardation).
(c) Ball thrown upward: Starting at some positive velocity $u$ (upward), a straight line with slope −g ≈ −9.8 m s⁻² decreasing to zero at the highest point (t = u/g), then continuing with the same slope into negative velocity as it falls back. The graph is a single straight line of constant negative slope passing through zero in the middle — symmetric about the x-axis if caught at the same height.
Q7 (Numerical). A bus starts from rest and reaches a velocity of 36 km h⁻¹ in 10 s. (a) What is the acceleration? (b) Is this uniform or non-uniform motion? (c) What kind of p-t graph will this produce?
Convert: $36\,\text{km h}^{-1} = 36 \times \frac{5}{18} = 10\,\text{m s}^{-1}$
(a) Acceleration:
$$a = \frac{v - u}{t} = \frac{10 - 0}{10} = 1\,\text{m s}^{-2}$$(b) Motion type: Non-uniform (speed is changing). More specifically, it is uniformly accelerated motion because acceleration is constant at 1 m s⁻².
(c) p-t graph: A parabola starting from origin (position and velocity both zero at t = 0), curving upward because position increases as $s = \frac{1}{2}at^2 = \frac{1}{2}(1)t^2 = 0.5t^2$ metres.
Force and Laws of Motion (Chapter 5) — Newton's first law explains why objects in uniform motion stay in uniform motion (inertia). Newton's second law links force to change in velocity, which is what produces non-uniform motion. The concepts here lay the groundwork for that chapter.