Motion in One Dimension Class 9 ICSE — Physics Chapter 2
This chapter on motion in one dimension class 9 ICSE builds the ideas every kinematics problem uses. It starts with scalar and vector quantities, then defines speed, velocity, acceleration, and the three motion graphs. It closes with motion under gravity and the equations of uniformly accelerated motion. The board frames this material around the official CISCE syllabus published for Class 9 Physics.
Download Motion in One Dimension Class 9 ICSE Physics Chapter 2 PDF
Download the Motion in One Dimension Class 9 ICSE Physics chapter PDF to revise offline or print for practice. It is the full chapter as printed in the book — 28 pages, 9 sections, 101 questions.
What is inside Chapter 2
28 pages · 9 sections · 2 worked examples · 101 exercise questions
| Section | Title |
|---|---|
| 2.1 | SCALAR AND VECTOR QUANTITIES |
| 2.2 | REST AND MOTION |
| 2.3 | DISTANCE AND DISPLACEMENT |
| 2.5 | ACCELERATION AND RETARDATION |
| 2.6 | DISPLACEMENT-TIME GRAPH |
| 2.7 | VELOCITY-TIME GRAPH |
| 2.8 | ACCELERATION – TIME GRAPH |
| 2.9 | MOTION UNDER GRAVITY |
| 2.9 | EQUATIONS OF UNIFORMLY ACCELERATED MOTION |
- EXERCISE 2(A): 28 questions
- Multiple choice type :: 21 questions
- EXERCISE 2 (B): 18 questions
- Multiple choice type :: 14 questions
- EXERCISE 2(C): 3 questions
- Multiple choice type :: 17 questions
2.1 SCALAR AND VECTOR QUANTITIES
Physical quantities fall into two broad classes. Scalar quantities are expressed by magnitude alone. A numerical value and a unit say everything, like 5.0 kg for mass. Pure numbers such as \pi carry no unit. Common scalars include mass, length, time, distance and speed.
Vector quantities need magnitude, unit and direction. “Displace a particle by 5 m” is incomplete until you name the direction. So a vector needs three parts: numerical value, unit, and direction. Examples include displacement, velocity, acceleration and force.
A vector’s magnitude is always positive. A negative sign shows the opposite direction. Arrows mark vectors, like \vec{v} for velocity, \vec{a} for acceleration and \vec{F} for force. So \vec{F} and -\vec{F} point in opposite directions. Scalars follow ordinary arithmetic; vectors follow their own rules.
Worked pattern: from the list “distance, force, time, velocity”, pick the scalars and vectors. Distance and time are scalars because they need no direction. Force and velocity are vectors because their meaning is complete only with a direction.
2.2 REST AND MOTION
A body is at rest when its position does not change relative to its immediate surroundings. It is in motion when that position does change. Nothing in the universe is truly at rest — the Earth moves around the Sun, and the Sun moves around its galaxy. Rest is always relative.
One dimensional motion is motion along a straight line, also called rectilinear motion. A train on a straight track and a stone falling vertically are examples. There is no sideways movement in one dimensional motion.
This motion is drawn along the x-axis in the direction of travel. Each point on the line is the body’s position at one instant. The x coordinate changes with time t.
Worked pattern: a marble dropped from rest has position x = 0 m at t = 0 s, 4 m at 1 s, and 16 m at 2 s. Plot these on the x-axis with a suitable scale. The growing gaps between points show the marble is speeding up.
2.3 DISTANCE AND DISPLACEMENT
Distance is the total length of the path a body travels. It is a scalar and always positive, and it depends on the path taken. Displacement is the shortest distance from the initial to the final position, directed from start to finish. It is a vector.
The magnitude of displacement is equal to or less than the distance. It is equal only when motion is in one fixed direction. Displacement can be positive or negative. It is zero when the body returns to its starting point.
\text{Speed } v = \frac{\text{Distance } S}{\text{Time } t} \tag{2.1}
S = v t \tag{2.2}
\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} \tag{2.3}
\vec{S} = \vec{v} \, t \tag{2.4} \qquad \text{Average velocity} = \frac{\text{Displacement}}{\text{Total time}} \tag{2.5}
Uniform speed means equal distances in equal time intervals. Variable speed does not. Instantaneous speed is the ratio taken over a very short interval. Average speed is total distance over total time. Speed is scalar; velocity is vector and carries direction.
| Distance | Displacement |
|---|---|
| Length of the path travelled | Shortest distance from start to finish |
| Scalar, always positive | Vector, positive or negative |
| Depends on the path | Independent of the path |
Worked pattern: a jogger runs 300 m east in 40 s, then returns to the start in 50 s. Speed on the first leg is 300/40 = 7.5 m s⁻¹. Total distance is 600 m and total time is 90 s, so average speed is 600/90 \approx 6.67 m s⁻¹. Displacement is zero, so average velocity is zero. You will reuse these definitions across the Class 9 ICSE Physics book.
2.5 ACCELERATION AND RETARDATION
Acceleration is the rate of change of velocity with time. Its SI unit is m s⁻². In straight line motion, direction does not change, so acceleration comes only from a change in speed. Increasing speed means accelerated motion; decreasing speed means retarded motion.
a = \frac{v - u}{t} \quad \text{or} \quad v = u + at \tag{2.7}
When the final velocity is greater than the initial velocity, a is positive — that is acceleration. When the final velocity is smaller, a is negative — that is retardation. Uniform acceleration means equal velocity changes in equal times. Variable acceleration means the changes are unequal.
Acceleration due to gravity g is the acceleration a freely falling body gains from the Earth’s pull. A falling body has +g; a rising body has -g. The average value is 9.8 m s⁻², about 10 m s⁻². The value of g does not depend on the mass of the body, so in vacuum a stone and a pencil fall together.
Worked pattern: a bicycle speeds from 4 m s⁻¹ to 10 m s⁻¹ in 3 s. Then a = (10 - 4)/3 = 2 m s⁻². A common mistake in this ICSE chapter is reading a negative a as backward motion. A negative acceleration only means velocity is decreasing with time.
2.6 DISPLACEMENT-TIME GRAPH
Time is on the x-axis and displacement on the y-axis. The slope of the graph gives velocity. A positive slope means moving away from the starting point. A negative slope means returning towards it.
Three cases matter. A line parallel to the time axis means the body is stationary. A straight inclined line means uniform velocity. A curve means variable velocity, and you read the velocity from the tangent drawn at that instant.
The graph can never be parallel to the displacement axis. That would mean displacement increases with no time passing, which is infinite velocity and impossible.
Worked pattern: a straight line passes through the points (2 s, 10 m) and (6 s, 40 m). Velocity is the slope: (40 - 10)/(6 - 2) = 30/4 = 7.5 m s⁻¹. The steeper the line, the higher the velocity.
2.7 VELOCITY-TIME GRAPH
Time is on the x-axis and velocity on the y-axis. The slope gives acceleration. The area enclosed with the time axis gives displacement. Area above the axis is positive displacement; area below it is negative displacement. Total distance is the arithmetic sum of both areas, ignoring signs.
Cases follow the same logic as the displacement-time graph. A line parallel to the time axis is uniform velocity with zero acceleration. A straight inclined line is uniform acceleration if the slope is positive, uniform retardation if negative. A curve means variable acceleration. The graph can never be parallel to the velocity axis because that would mean infinite acceleration.
Worked pattern: a car moves at 12 m s⁻¹ for 4 s, then brakes to a stop in 3 s. The first part is a rectangle: 4 \times 12 = 48 m. The braking part is a triangle: \frac{1}{2} \times 3 \times 12 = 18 m. Total distance is 48 + 18 = 66 m.
2.8 ACCELERATION – TIME GRAPH
Time is on the x-axis and acceleration on the y-axis. The area enclosed with the time axis gives the change in speed. So acceleration multiplied by time equals the change in speed.
Four cases appear. A line on the time axis means uniform velocity, so acceleration is zero. A line parallel above the axis means constant acceleration. A line parallel below the axis means constant retardation. A curve means variable acceleration.
Worked pattern: a constant acceleration of 3 m s⁻² acts for 5 s. The change in speed is 3 \times 5 = 15 m s⁻¹. A body starting at 2 m s⁻¹ therefore reaches 17 m s⁻¹.
2.9 MOTION UNDER GRAVITY
A freely falling body moves with uniform acceleration g, about 10 m s⁻². A body moving vertically upwards has uniform retardation g. Motion under gravity is therefore uniformly accelerated or uniformly retarded motion.
The acceleration-time graph is a line parallel to the time axis. Its area builds the velocity-time graph, a straight inclined line. The area of that graph builds the displacement-time graph, which is a curve. For a freely falling body, displacement is proportional to the square of time: S \propto t^2.
Plot S against t^2 and you get a straight line. Its slope is half of g. Doubling the slope gives g.
Edge case: the value of g changes from place to place. It is greatest at the poles and least at the equator, and it is independent of the mass of the falling body.
Worked pattern: with g = 10 m s⁻², a body from rest has velocity v = 10 \times 3 = 30 m s⁻¹ after 3 s. Its displacement is S = \frac{1}{2} \times 10 \times 9 = 45 m.
2.9 EQUATIONS OF UNIFORMLY ACCELERATED MOTION
Three equations connect initial velocity u, final velocity v, acceleration a, time t and displacement S for uniformly accelerated motion.
v = u + at \tag{2.9}
S = ut + \frac{1}{2}at^2 \tag{2.11}
v^2 = u^2 + 2aS \tag{2.13}
All three come from the velocity-time graph. The slope of the line gives the first equation. The area of the trapezium under the line gives the second and third. When the body starts from rest, u = 0, so the equations reduce to v = at, S = \frac{1}{2}at^2 and v^2 = 2aS (2.14).
When motion is retarded, a is negative, giving v = u - at, S = ut - \frac{1}{2}at^2 and v^2 = u^2 - 2aS (2.15).
Worked pattern: a scooter starts from rest with a = 3 m s⁻² for 6 s. Then v = 3 \times 6 = 18 m s⁻¹ and S = \frac{1}{2} \times 3 \times 36 = 54 m. The common mistake in Class 9 ICSE numericals is mixing units — convert km h⁻¹ to m s⁻¹ before using seconds. This same method appears across the whole Class 9 ICSE book list.
What to practise from Motion in One Dimension Class 9 ICSE
Work the exercise blocks in order. Each one tests a different part of the chapter, from definitions to graph reading to the equations of motion.
- EXERCISE 2(A): 28 questions on scalars, vectors, rest and motion, distance, displacement, speed, velocity, acceleration and retardation.
- Multiple choice type (Exercise 2(A)): 21 items.
- EXERCISE 2(B): 18 questions on the displacement-time, velocity-time and acceleration-time graphs.
- Multiple choice type (Exercise 2(B)): 14 items.
- EXERCISE 2(C): 3 questions on the equations of uniformly accelerated motion.
- Multiple choice type (Exercise 2(C)): 17 items.
Motion in One Dimension Class 9 ICSE frequently asked questions
When is displacement equal to distance in motion in one dimension class 9 icse?
When the body moves in one fixed direction along a straight line, the magnitude of displacement equals the distance. On a curved or zig-zag path, displacement is always smaller than the distance.
Why is the average velocity zero when a body returns to its starting point?
Average velocity is displacement divided by total time. When the final position matches the initial position, displacement is zero, so average velocity is zero. Average speed stays positive because the total distance is not zero.
What does the slope of a displacement-time graph give in motion in one dimension class 9 icse?
The slope gives the velocity at that instant. A positive slope means moving away from the start, a negative slope means returning towards it, and a zero slope means the body is stationary.
How do I find the distance travelled from a velocity-time graph?
Find the area enclosed between the graph and the time axis. For distance, add the areas without signs. For displacement, add the area above the axis and subtract the area below it.
Does the acceleration due to gravity depend on the mass of the falling body?
No. The value of g is the same for all masses, so in vacuum a stone and a pencil fall together. The value of g does vary from place to place — greatest at the poles and least at the equator.
Reference: ICSE Class 9 Physics textbook material, chapter 2: Motion in One Dimension — CISCE-aligned.