Kinematics Notes for Quick Revision 📚 - Equations, Graphs, and Applications

Kinematics is a branch of physics that describes the motion of objects without considering the forces or causes of motion. It forms the foundation for understanding concepts in mechanics and solving real-world problems involving motion.

This article provides detailed notes on kinematics, including definitions, equations of motion, graphical representation, and applications.

What is Kinematics?

Definition: Kinematics is the study of the motion of objects, including displacement, velocity, acceleration, and time, without considering the forces causing the motion.

Key Parameters:

• Position: The location of an object at a specific time.
• Displacement: The shortest straight-line distance between an object’s initial and final position.
• Velocity: The rate of change of displacement.
• Acceleration: The rate of change of velocity.

Types of Motion

1. Uniform Motion

Definition: Motion in which an object covers equal distances in equal intervals of time.

Characteristics:

• Velocity remains constant.
• Acceleration is zero.

2. Non-Uniform Motion

Definition: Motion in which an object covers unequal distances in equal intervals of time.

Characteristics:

• Velocity changes with time.
• Acceleration is non-zero.

3. Linear Motion

• Motion along a straight line.
• Example: A car moving on a straight road.

4. Projectile Motion

• Motion of an object under the influence of gravity after being projected.
• Example: A ball thrown in the air.

5. Circular Motion

• Motion along a circular path.
• Example: A satellite orbiting Earth.

Key Kinematics Parameters

1. Displacement ($\vec{s}$)

Definition: A vector quantity representing the shortest path between two points.

Unit: Meter (m).

2. Velocity ($\vec{v}$)

Definition: The rate of change of displacement.

Formula: $$\vec{v}=\frac{\mathrm{\Delta }\vec{s}}{\mathrm{\Delta }t}$$

• Unit: $\text{m/s}$.

3. Acceleration ($\vec{a}$)

Definition: The rate of change of velocity.

Formula: $$\vec{a}=\frac{\mathrm{\Delta }\vec{v}}{\mathrm{\Delta }t}$$

• Unit: $\text{m/s}^2$.

Equations of Motion

For objects moving with uniform acceleration, the following equations of motion apply:

First Equation:

$$v=u+at$$

Where:

• $v$: Final velocity.
• $u$: Initial velocity.
• $a$: Acceleration.
• $t$: Time.

Second Equation:

$$s=ut+\frac{1}{2}a{t}^2$$

Where:

• $s$: Displacement.

Third Equation:

$$v^2=u^2+2as$$

Fourth Equation (average velocity):

$$v_{\text{avg}}=\frac{u+v}{2}$$

Graphical Representation of Motion

1. Displacement-Time Graph

Slope: Represents velocity.

Characteristics:

• Straight line: Uniform motion.
• Curved line: Non-uniform motion.

2. Velocity-Time Graph

• Slope: Represents acceleration.
• Area under the curve: Represents displacement.

3. Acceleration-Time Graph

Area under the curve: Represents change in velocity.

Projectile Motion

Definition: The motion of an object under the influence of gravity after being projected at an angle.

Key Parameters:

Horizontal motion:

• Constant velocity ($v_x=u\cos \theta$).

Vertical motion:

• Uniformly accelerated motion ($v_y=u\sin \theta -gt$).

Equations:

• Time of flight: $$T=\frac{2u\sin \theta }{g}$$
• Maximum height: $$H=\frac{u^2{\sin }^2\theta }{2g}$$
• Range: $$R=\frac{u^2\sin 2\theta }{g}$$

Relative Motion

Definition: The motion of one object as observed from another moving object.

Relative Velocity:

• For two objects $A$ and $B$: $${\vec{v}}_{AB}={\vec{v}}_A-{\vec{v}}_B$$

Key Points to Remember

Scalar and Vector Quantities:

• Displacement, velocity, and acceleration are vectors.
• Distance and speed are scalars.

Sign Conventions:

Positive and negative signs indicate direction in 1D motion.

Uniform vs Non-Uniform Acceleration:

Equations of motion apply only for uniform acceleration.

Horizontal and Vertical Components:

Projectile motion can be analyzed separately in horizontal and vertical directions.

Applications of Kinematics

Transportation:

Designing speed limits and acceleration for vehicles.

Sports:

Calculating the trajectory of a ball.

Aerospace:

Understanding the motion of rockets and satellites.

Robotics:

Programming robotic motion in manufacturing.

FAQs About Kinematics

What is the difference between distance and displacement?

Distance is the total path length traveled (scalar), while displacement is the shortest straight-line distance between two points (vector).

Can velocity be negative?

Yes, velocity is negative when an object moves in the opposite direction to the reference axis.

What is the significance of the slope in a velocity-time graph?

The slope of a velocity-time graph represents acceleration.

Why do we study kinematics?

Kinematics provides a framework to describe motion, which is essential for understanding dynamics and real-world applications.

Kinematics is a fundamental branch of physics that deals with describing motion using displacement, velocity, acceleration, and time. By mastering the equations of motion, graphical analysis, and concepts like projectile and relative motion, students can build a strong foundation for solving complex problems in physics. These notes serve as an essential resource for academic and competitive exam preparation.

Explore related topics:

• Units and Dimensions
• Circular Motion
• Rotational Motion and Moment of Inertia