What is the difference between speed and velocity?

Speed is distance travelled per unit time and has no direction. Velocity is displacement per unit time and includes direction.

Why is uniform circular motion called accelerated motion?

Because although the speed stays the same, the direction of motion keeps changing, so the velocity vector changes continuously. Any change in velocity counts as acceleration.

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Chapter 1 · Class 9 · Physics · CBSE/NCERT

Motion

From cars and buses to satellites and circular motion, this chapter builds the complete language of movement: distance, displacement, speed, velocity, acceleration, graphs, and equations of motion.

DistanceDisplacementSpeedVelocityAccelerationGraphsCircular Motion

Complete Chapter Roadmap - 14 Topics

01What is Motion?02Distance Travelled 03Displacement 04Scalar vs Vector 05Uniform and Non-Uniform Motion 06Speed and Average Speed 07Velocity and Average Velocity 08Acceleration and Retardation 09Equations of Motion 10Distance-Time Graphs 11Speed-Time Graphs 12Graphical Derivation 13Uniform Circular Motion 14Chapter Summary

What is Motion?

Position change with respect to a reference point

Key Idea

Without a reference point, we cannot say whether a body is moving or at rest.

A body is said to be in motion when its position changes continuously with respect to a stationary object taken as a reference point.

A parked desk in a classroom is stationary. A car moving past the school gate changes its position with respect to the building, so it is in motion.

Motion is always relative. A passenger sitting inside a moving train is at rest with respect to the train seat, but in motion with respect to trees and buildings outside.

Think About It

Is a passenger sitting in a moving train at rest or in motion?

Answer: Both answers are possible, depending on the chosen reference point.

Distance Travelled

The total length of the actual path covered

Formula

\text{Distance} = \text{Total path length covered}

Distance is the actual length of the path covered by a moving body, regardless of direction.

If a person walks 3 km east, then 4 km north, and then 3 km west, the total distance covered is

3 + 4 + 3 = 10 \text{ km}

Distance is always positive and is a scalar quantity because it has magnitude only.

Displacement

Shortest straight-line path from start to finish

Important Rule

Displacement is a vector quantity, and it is always less than or equal to distance.

Displacement is the shortest distance between the initial and final position of a body, along with direction.

A body may travel a large distance but still have small displacement if it ends close to where it started.

Displacement can be zero when the final position is the same as the initial position, even if distance travelled is large.

Worked Example

Path vs straight-line movement

A man walks 1.5 m east, then 2 m south, and then 4.5 m east. Total distance = 8 m, but displacement is the straight-line distance from start to finish, which is about

\sqrt{6^2 + 2^2} = \sqrt{40} \approx 6.3 \text{ m}

Scalar vs Vector Quantities

Direction decides the category

A scalar quantity has magnitude only. Examples: distance, speed, mass, time, and temperature.

A vector quantity has both magnitude and direction. Examples: displacement, velocity, acceleration, and force.

In this chapter, distance and speed are scalars, while displacement, velocity, and acceleration are vectors.

Uniform and Non-Uniform Motion

Equal distances in equal times or not

A body is in uniform motion if it covers equal distances in equal intervals of time.

A body is in non-uniform motion if it covers unequal distances in equal intervals of time.

Uniform motion appears as a straight line on a distance-time graph. Non-uniform motion appears as a curve.

Quick Check

A freely falling ball covers 4.9 m, 14.7 m, and 24.5 m in successive 1-second intervals. Is this uniform?

Answer: No. The distances in equal time intervals are unequal, so the motion is non-uniform.

Speed and Average Speed

Distance covered per unit time

Unit

The SI unit of speed is m/s, though km/h is also commonly used in daily life.

Speed tells us how much distance is covered in a unit of time.

The formula for speed is

v = \frac{s}{t}

where

s

is distance travelled and

t

is time taken.

Average speed is used when the speed is not constant and is given by

\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}

Solved Example

Two different speeds on one journey

A car travels 30 km at 40 km/h and the next 30 km at 20 km/h. Total time

= \frac{30}{40} + \frac{30}{20} = \frac{3}{4} + \frac{3}{2} = \frac{9}{4} \text{ h}

Average speed

= \frac{60}{9/4} = \frac{240}{9} \approx 26.6 \text{ km/h}

Velocity and Average Velocity

Displacement per unit time

Exam Trap

Average speed and average velocity are not the same. If displacement is zero, average velocity becomes zero, but average speed may still be positive.

Velocity is speed in a given direction. It is defined as displacement per unit time.

The formula is

v = \frac{\text{Displacement}}{t}

and average velocity is

\bar{v} = \frac{\text{Total Displacement}}{\text{Total Time}}

A body can have zero average velocity but non-zero average speed if it returns to the starting point.

Acceleration and Retardation

Rate of change of velocity

Average Velocity Formula

When acceleration is uniform, average velocity can also be written as

\bar{v} = \frac{u+v}{2}

Acceleration tells us how quickly velocity changes with time.

The formula is

a = \frac{v-u}{t}

where

u

is initial velocity,

v

is final velocity, and

t

is time.

When velocity decreases, acceleration is negative. This is called retardation or deceleration.

Quick Practice

A driver decreases speed from 25 m/s to 10 m/s in 5 s. Find acceleration.

Answer:

a = \frac{10-25}{5} = -3 \text{ m/s}^2

Three Equations of Motion

The core formulas of uniformly accelerated motion

These equations apply only when acceleration is uniform.

The three equations are

v = u + at

s = ut + \frac{1}{2}at^2

v^2 = u^2 + 2as

Choose the equation according to which quantity is missing. For example, when time is not given, the third equation is usually the most helpful.

Solved Example

Car starting from rest

A racing car starts from rest with acceleration

4\text{ m/s}^2

for 10 s. Since

u=0

and

s = ut + \frac{1}{2}at^2

, we get

s = 0 + \frac{1}{2}(4)(10)^2 = 200 \text{ m}

Show one more equations-of-motion example

A scooter moving at 10 m/s is stopped by brakes producing acceleration -0.5 m/s². Find the stopping distance.

Use $v^2 = u^2 + 2as$ with $u=10$ , $v=0$ , $a=-0.5$ .

$0 = 100 - s$ , so $s = 100$ m.

Distance-Time Graphs

Reading motion visually

In a distance-time graph, time is plotted on the x-axis and distance on the y-axis.

The slope of the graph gives the speed:

\text{Speed} = \frac{\Delta d}{\Delta t}

A straight line means uniform speed, a horizontal line means the body is at rest, and a curved line indicates non-uniform motion.

Speed-Time Graphs

Slope gives acceleration, area gives distance

In a speed-time graph, the slope gives acceleration:

a = \frac{\Delta v}{\Delta t}

The area under the speed-time graph gives the distance travelled.

A horizontal line means constant speed, a line sloping upward means positive acceleration, and a line sloping downward means retardation.

Key Rule

Why area matters

If speed is constant for a time interval, the graph forms a rectangle. Rectangle area = base × height = time × speed, which is exactly the distance travelled.

Use a speed-time graph to find distance

If a body moves with constant speed 6 m/s for 6 seconds, the speed-time graph forms a rectangle.

Distance = area under graph = base × height = 6 × 6 = 36 m.

Graphical Derivation of Equations

Proving the motion equations using a velocity-time graph

From the slope of the velocity-time graph, we derive

v = u + at

From the area of the rectangle and triangle under the graph, we derive

s = ut + \frac{1}{2}at^2

Using area again together with the first equation, we derive

v^2 = u^2 + 2as

This graphical view helps you understand that the equations come from geometry as well as algebra.

Uniform Circular Motion

Constant speed but changing direction

Examples

Examples include the tip of the second hand of a clock, satellites orbiting Earth, and a cyclist moving around a circular track at constant speed.

When a body moves along a circular path with constant speed, its motion is called uniform circular motion.

Even though speed is constant, the direction changes continuously, so velocity changes continuously. That means the body is accelerated.

The speed in one complete revolution is

v = \frac{2\pi r}{t}

where

r

is radius and

t

is time period.

Complete Chapter Summary

The formulas and rules you should revise before exams

Distance = total path length. Displacement = shortest distance with direction.

Speed = distance/time. Velocity = displacement/time. Acceleration = change in velocity/time.

The three equations of motion are

v = u + at

s = ut + \frac{1}{2}at^2

v^2 = u^2 + 2as

For graphs: distance-time slope gives speed, speed-time slope gives acceleration, and speed-time area gives distance.

Motion: revision sheet

Close the notes and explain each idea in your own words. Then check the formulas and attempt the examples before opening their solutions.

Recall checklist

Distance, Displacement, Speed, and Velocity
Uniform and Non-Uniform Motion, Acceleration
Three Equations of Motion
Graphs and Uniform Circular Motion

For each topic: state the rule, explain when it applies, give an example and identify one mistake to avoid. Return to any topic you cannot explain without looking.

Formula recap (4)

Uniform and Non-Uniform Motion, Acceleration

a = \frac{v - u}{t}

a = acceleration, v = final velocity, u = initial velocity.

Three Equations of Motion

v = u + at

Three Equations of Motion

s = ut + \frac{1}{2}at^2

Three Equations of Motion

v^2 = u^2 + 2as

Explain your method

Write the given information, choose a method, show the steps, then check units and whether the answer makes sense.

A body starts from rest and reaches 20 m/s in 10 seconds. Find its acceleration.

Check worked solution 1

Using a = (v - u) / t = (20 - 0) / 10, the acceleration is 2 m/s².

Apply the concept, avoid the trap

Common mistake: Treating average speed and the magnitude of average velocity as interchangeable.

Use this reasoning: Average speed uses total distance. Average velocity uses displacement, including direction. Both divide by total elapsed time.

Worked application

A student walks 120 m east in 60 s, then 80 m west in 40 s. Find the average speed and average velocity for the whole trip.

Reveal the method and checks

Total distance = 120 + 80 = 200 m. Total time = 60 + 40 = 100 s. Average speed = 200/100 = 2 m/s.
Taking east as positive, displacement = 120 − 80 = 40 m east. Average velocity = 40/100 = 0.4 m/s east.
The return leg increases distance but reduces displacement. Keeping a sign convention prevents the two totals from being confused.

Check your understanding

If the student returns all the way to the start after 120 s, is the average speed zero?

Check your reasoning

No. The total distance is 240 m, so average speed is 2 m/s. Displacement is zero, so average velocity is zero.

Turn mistakes into revision

Record the question, the step that went wrong and the corrected reason. Try it again tomorrow without the solution, then revisit it after a week. A correct guess still needs an explanation.

Practise this chapter