Motion Along a Straight Line

Learning Outcomes

This chapter introduces the fundamental concepts of kinematics, focusing on motion along a straight line. Students will learn to:

• Describe straight-line motion using displacement and average velocity.

• Distinguish between instantaneous velocity and speed.

• Apply average and instantaneous acceleration to analyze changes in velocity.

• Solve problems involving free fall under gravity.

• Analyze straight-line motion with non-constant acceleration.

Introduction to Kinematics

Kinematics is the branch of physics that studies the motion of objects without considering the causes of motion (forces). The primary quantities in kinematics are velocity and acceleration.

• Velocity describes how fast and in what direction an object moves.

• Acceleration describes how the velocity of an object changes over time.

• Example: In a sprinting race, a runner accelerates at the start, maintains speed, and decelerates after crossing the finish line.

Displacement, Time, and Average Velocity

Definitions and Formulas

When a particle moves along the x-axis, its position is given by the coordinate x. The change in position is called displacement:

• Displacement:

• Time Interval:

• Average x-velocity:

Key Points:

• Displacement is a vector quantity; it has both magnitude and direction.

• Average velocity is also a vector and depends on the total displacement and total time.

• Speed is the magnitude of velocity but does not include direction.

• Example: If a swimmer covers 50 m in 25 s, .

Rules for the Sign of X-Velocity

The sign of velocity indicates the direction of motion along the x-axis. The following table summarizes the rules:

Example: If a particle's x-coordinate changes from –5 m to –3 m, it is moving in the +x-direction (since the value is increasing).

Additional info:

• These notes are based on textbook slides and cover the essential concepts for understanding one-dimensional kinematics in introductory college physics.