1. Force

Force is a physical cause that changes or tends to change the state of an object. It can change the speed, direction, shape, or size of an object.

Types of Force

• Contact Force (e.g., frictional force, tension)
• Non-contact Force (e.g., gravitational force, magnetic force)

2. Balanced and Unbalanced Force

Balanced Force: When two or more forces acting on a body cancel each other, and there is no change in motion.

Example: A book lying on a table.

Unbalanced Force: When forces acting on a body are not equal, resulting in a change in motion or direction.

Example: Kicking a football.

3. Motion and Velocity

Motion: A body is said to be in motion if it changes its position with respect to a reference point.

Velocity: The rate of change of displacement. It includes direction.

• Uniform Velocity: Equal displacement in equal time intervals.
• Non-uniform Velocity: Unequal displacement in equal time intervals.

4. Acceleration and Retardation

Acceleration (a): Rate of change of velocity.

Retardation: Negative acceleration (velocity decreases with time).

5. Graphical Representation of Linear Motion

a. Displacement-Time Graph

• Straight Line with Positive Slope: Uniform motion
• Curve: Non-uniform motion
• Horizontal Line: Body is at rest

b. Velocity-Time Graph

• Horizontal Line: Uniform velocity
• Sloped Line: Accelerated motion
• Area under graph: Displacement
• Slope of graph: Acceleration

1. Displacement-Time (s-t) Graphs

(a) Uniform Velocity 

• Graph: Straight line with a constant slope (positive or negative).
• Interpretation: Slope = Velocity (v=Δs/Δt). Steeper slope = Higher velocity.

Example: A car moves 20 m in 5 s at constant speed. Velocity (v) = 20 m/5 s = 4 m/s.

(b) Non-Uniform Velocity (Accelerated Motion)

• Graph: Curved line (parabola for constant acceleration).
• Interpretation: Changing slope = Changing velocity (acceleration).

Example: A car starts from rest and accelerates, covering: 0 m at 0 s, 5 m at 2 s, 20 m at 4 s

2. Velocity-Time (v-t) Graphs

(a) Uniform Acceleration

• Graph: Straight line with positive slope.
• Interpretation: Slope = Acceleration (a=Δv/Δt). Area under graph = Displacement.

Example: A car accelerates from 10 m/s to 30 m/s in 5 s. Acceleration (a) = (30−10)/5 = 4 m/s².

(b) Uniform Retardation (Deceleration)

• Graph: Straight line with negative slope.
• Interpretation: Slope = Negative acceleration (slowing down).

Example: A car slows from 20 m/s to 0 m/s in 4 s. Retardation = (0−20)/4 = −5 m/s².

(c) Constant Velocity (Zero Acceleration)

• Graph: Horizontal line (slope = 0).
• Interpretation: Velocity remains unchanged (no acceleration).

Example: A car moves at 15 m/s for 6 seconds.

6. Equations of Motion

Where:

u = initial velocity,

v = final velocity,

s = displacement,

a = acceleration,

t = time

Derive v = u + at

Given:

• v = final velocity (in m/s)
• u = initial velocity (in m/s)
• a = constant acceleration (in m/s²)
• t = time (in seconds)

Acceleration (a) is the rate of change of velocity with time:

a = Change in velocity / Time taken

or, a = (v − u) / t

or, at = v – u

or, v = u + at Derived

Derive s = {(u + v) × t} / 2

Given

• s = displacement (in meters)
• u = initial velocity (in m/s)
• v = final velocity (in m/s)
• t = time (in seconds)

Concept of Average Velocity

For motion with constant acceleration, the average velocity is the arithmetic mean of initial and final velocities:

Average Velocity = (u + v) / 2

Relationship Between Displacement, Average Velocity, and Time

Displacement (s) is given by:

Displacement = Average Velocity × Time

Substitute the average velocity:

s = (u + v) / 2 × t

Derived

Derive s = ut + ½ at²

Given:

• v = final velocity (in m/s)
• u = initial velocity (in m/s)
• a = constant acceleration (in m/s²)
• t = time (in seconds)
• s = displacement (in meters)

Using Average Velocity

Average velocity for constant acceleration:

v = (u + v) / 2

or, v = {u + (u + at)} / 2

or, v = (2u + at) / 2

Displacement = Average velocity × time:

s = (2u + at) / 2 × t

or, s = 2ut/2 + at²/2

or, s = ut + ½ at²

Derived

7. Inertia

Inertia is the property of a body to resist changes in its state of rest or uniform motion.

Types of Inertia

Inertia of Rest: A body at rest remains at rest unless acted upon.

Examples:

Inertia of Motion: A moving object continues in motion unless stopped.

Examples

8. Newton's Laws of Motion

First Law (Law of Inertia)

A body remains at rest or in uniform motion in the straight line unless acted upon by an external force.

Second Law (Law of Acceleration)

The force acting on a body is equal to the product of its mass and acceleration.

F = ma

Let a body of mass (m) has moved from a point to another point. Let its acceleration be 'a'.

Acceleration of the body is:

• Directly proportional to force applied.
• Inversely proportional to mass of the body.

From above equations, we get

a ∝ f/m

or, f ∝ ma

or, f = kma (where k is proportionality constant)

If 1 N force is applied to the body of mass 1 kg accelerating 1 m/s², at that time value of k is also 1. Putting the value of k in equation 3, we get

f = ma

Third Law (Action and Reaction)

For every action, there is an equal and opposite reaction.

Examples:

9. Elasticity and Plasticity

Elasticity: The ability of an object to return to its original shape after the removal of deforming force.

Example: Rubber band

Plasticity: The inability of an object to return to its original shape after deformation.

Example: Clay

10. Numerical Problems (Examples)