Motion in a Straight Line Important Formulas, Definitions, and Examples | 11th Physics

Chapter 3: Motion in a Straight Line

Physics, Formulas, Motion, Kinematics, Distance, Displacement, Velocity, Acceleration, Equations

Introduction

In this chapter, we explore motion along a straight line, which is the simplest form of motion. It is described using quantities like displacement, velocity, and acceleration. The equations of motion derived in this chapter help predict future motion when initial conditions are known.

1. Displacement and Distance

Definition:

Distance is the total path length traveled by an object, while displacement refers to the shortest distance between the initial and final positions of the object. Displacement is a vector quantity, and distance is a scalar quantity.

Formula:

Displacement (s) is calculated as:

s = x₂ - x₁

Where x₂ is the final position and x₁ is the initial position.

2. Velocity

Definition:

Velocity is the rate of change of displacement with respect to time. It is a vector quantity, which means it has both magnitude and direction.

Formula:

The velocity (v) can be calculated using the formula:

v = (x₂ - x₁) / t

Where t is the time taken for the displacement to occur.

Types of Velocity:

• Average Velocity: The total displacement divided by the total time.
• Instantaneous Velocity: The velocity at a specific moment in time.

3. Acceleration

Definition:

Acceleration is the rate of change of velocity with respect to time. It is a vector quantity.

Formula:

Acceleration (a) is given by:

a = (v₂ - v₁) / t

Where v₂ is the final velocity, v₁ is the initial velocity, and t is the time taken for the change in velocity.

4. Equations of Motion

The equations of motion describe the relationship between displacement, velocity, acceleration, and time for an object moving with uniform acceleration.

Key Equations of Motion:

1. Equation 1: v = u + at
   Where:
   v = final velocity
   u = initial velocity
   a = acceleration
   t = time
2. Equation 2: s = ut + ½at²
   Where:
   s = displacement
3. Equation 3: v² = u² + 2as
   Where:
   v = final velocity
   u = initial velocity
   a = acceleration
   s = displacement

5. Graphical Representation of Motion

Motion can be represented graphically using three types of graphs: displacement-time, velocity-time, and acceleration-time graphs. These graphs help visualize how motion changes over time.

Key Graphs:

• Displacement-Time Graph: Shows how displacement changes with time.
• Velocity-Time Graph: Shows how velocity changes with time. The slope of the velocity-time graph gives acceleration.
• Acceleration-Time Graph: Shows how acceleration changes with time. A horizontal line indicates uniform acceleration.

6. Uniform and Non-Uniform Motion

Definition:

Uniform motion occurs when an object travels equal distances in equal intervals of time, while non-uniform motion occurs when the object covers unequal distances in equal intervals of time.

7. Important Definitions

• Displacement: The shortest distance between two points in a specific direction.
• Velocity: The rate of change of displacement with respect to time.
• Acceleration: The rate of change of velocity with respect to time.
• Uniform Motion: Motion where equal distances are covered in equal time intervals.
• Non-Uniform Motion: Motion where unequal distances are covered in equal time intervals.

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