CBSE Class 11 Physics Revision Notes Chapter 2: Motion in a Straight Line

Motion in a Straight Line describes how an object’s position, velocity and acceleration change along one axis. For CBSE Class 11 Physics, the chapter connects motion graphs with equations used for uniform acceleration and relative motion.

Motion is the change in an object’s position with time. When this change occurs along one line, the motion is called straight-line or rectilinear motion.

These CBSE Class 11 Physics Revision Notes Chapter 2 follow the current 2026–27 chapter. The Class 11 Physics Chapter 2 notes cover displacement, velocity, acceleration, motion graphs, kinematic equations and relative velocity.

Key Takeaways

• Straight-line motion: Position changes along one chosen axis.
• Instantaneous velocity: It equals the slope of the tangent to a position-time graph.
• Acceleration: It measures the rate of change of velocity with time.
• Velocity-time graph: Its slope gives acceleration, while its area gives displacement.

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Access Class 11 Physics Chapter 2 Motion in a Straight Line Notes in 30 Minutes

The chapter on Motion in a Straight Line Class 11 explains motion using position, time, velocity and acceleration. It then connects these quantities through graphs and equations.

Motion, Rest and Position in One Dimension

Motion is always described with respect to an observer or reference point. The same object may appear at rest to one observer and moving to another.

Motion and Rest

An object is in motion when its position changes with time relative to a chosen reference point.

An object is at rest when its position does not change relative to that reference point.

A passenger sitting inside a moving train is at rest relative to another passenger. The passenger is in motion relative to a person standing beside the track.

Frame of Reference

A frame of reference includes a coordinate system and a clock used to describe motion.

For motion along the x-axis:

• Positions to the right of the origin are usually positive.
• Positions to the left are usually negative.
• The origin and positive direction are chosen before solving the problem.

The signs of displacement, velocity and acceleration depend on this choice.

Point Object

An object can be treated as a point object when its size is much smaller than the distance it travels.

For example, a car travelling several kilometres may be treated as a point object. Its physical size is negligible compared with the distance covered.

Position

Position shows the location of an object relative to the chosen origin.

If an object lies 5 m to the right of the origin:

x = +5 m

If it lies 3 m to the left:

x = -3 m

Displacement

Displacement is the change in position of an object.

Displacement = Final position - Initial position

Δx = x₂ - x₁

Suppose an object moves from x₁ = 2 m to x₂ = 8 m.

Δx = 8 - 2

Δx = +6 m

The positive sign shows motion in the chosen positive direction.

Distance and Displacement in Motion in a Straight Line

Distance and displacement describe different aspects of motion.

Distance depends on the complete path followed. Displacement depends only on the initial and final positions.

Distance

Distance is the total length of the path travelled by an object.

It is a scalar quantity. Therefore, it has magnitude but no direction.

Distance is always positive or zero.

Displacement

Displacement is the shortest directed distance between the initial and final positions.

It is a vector quantity. In one-dimensional motion, its direction is shown through a positive or negative sign.

Displacement can be:

• Positive
• Negative
• Zero

Distance and Displacement Comparison

Suppose a person walks 5 m east and then 5 m west.

Distance = 5 + 5 = 10 m

Displacement = 0 m

The person returns to the starting point, so the final and initial positions are the same.

Speed and Velocity in Class 11 Physics Chapter 2

Speed and velocity describe how rapidly an object moves. Velocity also includes the direction of motion.

Average Speed

Average speed is the total distance travelled divided by the total time taken.

Average speed = Total distance/Total time

Its SI unit is metre per second, written as m s⁻¹.

Average speed is always positive or zero.

Average Velocity

Average velocity is the total displacement divided by the total time interval.

Average velocity = Total displacement/Total time

vavg = Δx/Δt

Suppose an object moves from x = 2 m to x = 14 m in 4 s.

Displacement = 14 - 2 = 12 m

Average velocity = 12/4

Average velocity = 3 m s⁻¹

Difference Between Average Speed and Average Velocity

The average speed is always greater than or equal to the magnitude of average velocity.

Instantaneous Velocity

Average velocity describes motion over a time interval. Instantaneous velocity gives the velocity at a particular instant.

It is defined as:

v = lim(Δt→0) Δx/Δt

In differential form:

v = dx/dt

Instantaneous velocity is the rate of change of position with time at that instant.

Instantaneous Speed

Instantaneous speed is the magnitude of instantaneous velocity.

If:

v = -24 m s⁻¹

Then:

Speed = 24 m s⁻¹

The negative sign in velocity shows direction. It does not mean that the object has negative speed.

Position-Time Graphs for Straight-Line Motion

A position-time graph shows how an object’s position changes with time.

Time is plotted along the horizontal axis. Position is plotted along the vertical axis.

Object at Rest

For an object at rest, position remains constant.

Its position-time graph is a horizontal straight line parallel to the time axis.

Slope = 0

Therefore:

Velocity = 0

Uniform Motion

In uniform motion, an object covers equal displacements in equal time intervals.

The position-time graph is a straight inclined line.

A constant slope shows constant velocity.

Non-Uniform Motion

In non-uniform motion, velocity changes with time.

The position-time graph is curved because its slope changes at different points.

Slope of a Position-Time Graph

The slope of a position-time graph gives velocity.

Slope = Change in position/Change in time

Velocity = Δx/Δt

For a curved graph, the slope of the tangent at a point gives instantaneous velocity.

A steeper graph represents a greater magnitude of velocity.

Acceleration and Velocity-Time Graphs

Velocity may change in magnitude, direction or both. Acceleration describes this change with time.

Average Acceleration

Average acceleration is the change in velocity divided by the time interval.

Average acceleration = Change in velocity/Time interval

aavg = Δv/Δt

aavg = (v₂ - v₁)/(t₂ - t₁)

The SI unit of acceleration is m s⁻².

Instantaneous Acceleration

Instantaneous acceleration is the acceleration at a particular instant.

a = lim(Δt→0) Δv/Δt

In differential form:

a = dv/dt

It is the slope of the tangent to the velocity-time graph at that instant.

Positive, Negative and Zero Acceleration

Acceleration can be positive, negative or zero.

The sign of acceleration alone does not show whether speed is increasing or decreasing.

A falling object can have negative acceleration and still speed up. This happens when the upward direction is chosen as positive.

Velocity-Time Graph

A velocity-time graph shows how velocity changes with time.

The slope of the graph gives acceleration:

Slope = Δv/Δt

The area under the graph gives displacement:

Displacement = Area under the velocity-time graph

Area Under a Velocity-Time Graph

For an object moving with constant velocity u for time T:

Displacement = uT

On the velocity-time graph, this equals the area of the rectangle under the graph.

The area may be positive or negative depending on the position of the graph relative to the time axis.

Kinematic Equations for Uniformly Accelerated Motion

For uniformly accelerated motion, acceleration remains constant.

The kinematic equations connect:

• Initial velocity, u
• Final velocity, v
• Acceleration, a
• Time, t
• Displacement, s

These equations apply only when acceleration is constant.

First Kinematic Equation

The first equation connects velocity, acceleration and time:

v = u + at

Use it when displacement is not required.

Rearranged forms include:

a = (v - u)/t

t = (v - u)/a

Second Kinematic Equation

The second equation connects displacement with time:

s = ut + ½at²

Use it when final velocity is not given or required.

If the object starts from rest:

u = 0

Therefore:

s = ½at²

Third Kinematic Equation

The third equation does not contain time:

v² = u² + 2as

Use it when time is not given.

Rearranged form:

s = (v² - u²)/2a

Average Velocity for Constant Acceleration

For constant acceleration:

Average velocity = (u + v)/2

Therefore:

s = [(u + v)/2]t

This relation is valid only when acceleration is constant.

Kinematic Formula Selection Table

Example Based on Uniform Acceleration

A car starts with a velocity of 5 m s⁻¹ and accelerates at 2 m s⁻² for 4 s.

Given:

u = 5 m s⁻¹
a = 2 m s⁻²
t = 4 s

Final velocity:

v = u + at

v = 5 + (2 × 4)

v = 13 m s⁻¹

Displacement:

s = ut + ½at²

s = (5 × 4) + ½(2)(4²)

s = 20 + 16

s = 36 m

Motion Under Gravity and Free Fall

An object released near Earth moves downward due to gravity.

When air resistance is neglected, the motion is called free fall.

Near Earth’s surface:

g = 9.8 m s⁻²

For many calculations, it may be taken as:

g = 10 m s⁻²

Sign Convention in Vertical Motion

The sign of g depends on the chosen positive direction.

If upward is positive:

a = -g

If downward is positive:

a = +g

The sign convention must remain consistent throughout the calculation.

Equations for Free Fall

For an object released from rest:

u = 0

Taking downward as positive:

v = gt

s = ½gt²

v² = 2gs

Free fall is a case of uniformly accelerated motion.

Vertically Upward Motion

For a body thrown upward, take upward as positive.

Then:

a = -g

The equations become:

v = u - gt

s = ut - ½gt²

v² = u² - 2gs

At the maximum height:

v = 0

The acceleration is still:

a = -g

Therefore, an object can have zero velocity at an instant while its acceleration remains non-zero.

Maximum Height

At maximum height:

v = 0

Using:

v² = u² - 2gH

0 = u² - 2gH

Therefore:

H = u²/2g

Time to Reach Maximum Height

Using:

v = u - gt

At maximum height:

0 = u - gt

Therefore:

t = u/g

Relative Velocity in One Dimension

Relative velocity describes the velocity of one object as observed from another moving object.

For two objects A and B:

Velocity of A relative to B:

vAB = vA - vB

Velocity of B relative to A:

vBA = vB - vA

Therefore:

vAB = -vBA

Objects Moving in the Same Direction

If two objects move in the same direction, their relative speed is the difference between their speeds.

Relative speed = Faster speed - Slower speed

Suppose:

vA = 20 m s⁻¹
vB = 12 m s⁻¹

Then:

vAB = 20 - 12

vAB = 8 m s⁻¹

Objects Moving in Opposite Directions

If two objects move in opposite directions, assign signs according to the chosen axis.

Suppose A moves right at 20 m s⁻¹ and B moves left at 12 m s⁻¹.

Take right as positive:

vA = +20 m s⁻¹
vB = -12 m s⁻¹

Then:

vAB = 20 - (-12)

vAB = 32 m s⁻¹

Their relative speed is the sum of their speeds.

Motion in a Straight Line Formula Table

Graph-Based Quick Revision

A straight line does not always represent uniform motion. Its meaning depends on the quantities plotted on the axes.

Important Terms from Chapter 2

Motion: Change in position of an object with time.

Rectilinear motion: Motion along a straight line.

Frame of reference: A coordinate system and clock used to describe motion.

Point object: An object whose size is negligible compared with the distance travelled.

Distance: Total path length travelled by an object.

Displacement: Directed change from initial position to final position.

Average velocity: Total displacement divided by total time.

Instantaneous velocity: Rate of change of position at a particular instant.

Acceleration: Rate of change of velocity with time.

Uniform acceleration: Equal changes in velocity during equal time intervals.

Free fall: Motion under gravity when air resistance is neglected.

Relative velocity: Velocity of one object measured with respect to another object.

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