Linear Motion

Introduction

This chapter introduces the fundamental concepts of linear motion in physics, focusing on how objects move in a straight line. Key topics include the relativity of motion, speed, velocity, acceleration, and free fall. Understanding these concepts is essential for analyzing and predicting the behavior of moving objects.

Motion Is Relative

Relativity of Motion

Motion is always described relative to a chosen reference point or frame. The observed movement of an object depends on the observer's own motion and position.

• Reference Frame: The perspective from which motion is measured (e.g., Earth, Sun).

• Example: If you walk on the road, your motion is relative to Earth. However, Earth itself is moving relative to the Sun, so your motion relative to the Sun is different from your motion relative to Earth.

Speed

Definition and Calculation

Speed is defined as the distance covered per unit of time. It is a scalar quantity, meaning it has magnitude but no direction.

• Formula:

• Units: Meters per second (m/s).

• Example: A girl runs 4 meters in 2 seconds. Her speed is .

Average Speed

Average speed is the total distance covered divided by the total time taken. It does not reflect variations in speed during the journey.

• Formula:

• Example: Driving 200 km in 2 hours gives an average speed of .

Instantaneous Speed

Instantaneous speed is the speed of an object at a specific moment in time. It can be measured using a speedometer.

• Example: When driving, your instantaneous speed may vary as you accelerate or decelerate, and is shown on your car's speedometer.

Velocity

Definition and Properties

Velocity is a vector quantity that describes both the instantaneous speed and the direction of travel. It is often referred to as "directed speed."

• Magnitude: The speed of the object.

• Direction: The direction in which the object is moving.

• Formula:

• Constant Velocity: Requires both constant speed and constant direction (straight-line motion).

• Velocity vs. Speed: Velocity changes if either speed or direction changes, while speed only changes with magnitude.

Acceleration

Definition and Calculation

Acceleration is the rate at which velocity changes over time. It can result from changes in speed, direction, or both.

• Formula:

• Units: Meters per second squared (m/s2).

• Example: A car making a turn experiences acceleration due to the change in direction, even if its speed remains constant.

Galileo's Experiments

Galileo studied acceleration using inclined planes. He found that steeper inclines result in greater acceleration, and that vertical free fall represents maximum acceleration.

• When air resistance is negligible, all objects fall with the same acceleration.

Free Fall

Definition and Acceleration Due to Gravity

Free fall refers to motion under the influence of gravity alone, with negligible air resistance. On Earth, the acceleration due to gravity is approximately (more precisely, ).

• All objects in free fall accelerate at the same rate, regardless of mass.

Velocity in Free Fall

The velocity acquired by an object starting from rest during free fall is given by:

• Example: After 1 second, ; after 2 seconds, ; after 3 seconds, .

Distance in Free Fall

The distance covered by an accelerating object starting from rest is:

• Example: After 4 seconds, .

Summary Table: Key Quantities in Linear Motion

Additional info: The acceleration due to gravity is more precisely , but is often used for simplicity in introductory physics problems.