Motion Along a Straight Line (1D Kinematics)

Introduction to Kinematics

Kinematics is the branch of physics that describes the motion of objects without considering the causes of motion. In one-dimensional (1D) kinematics, we focus on motion along a straight line, using a coordinate system to specify positions and directions.

• Frame of Reference: A system for specifying the precise location of objects in space and time. The origin and direction (positive/negative) must be defined.

• Key Quantities:

  • Position x(t): Where an object is at a particular time, relative to the origin. Units: meters (m), centimeters (cm), etc.

  • Velocity v(t): The rate at which position changes with time. Units: meters per second (m/s), kilometers per hour (km/h).

  • Acceleration a(t): The rate at which velocity changes with time. Units: meters per second squared (m/s2).

Average Quantities

To analyze motion, we often consider how quantities change over intervals of time.

• Change in a Quantity: (where can be position, velocity, etc.)

• Elapsed Time:

• Average Rate of Change: (dimensions depend on )

Position, Distance, and Displacement

Setting Up a Coordinate System

Before solving any motion problem, establish a coordinate system:

• Draw a diagram of the situation.

• Choose the origin () and decide which direction is positive.

• Label initial () and final () positions.

Displacement and Distance

• Displacement (): The change in position of an object. It is a vector and can be positive or negative.

  • Formula:

• Distance: The total length of the path traveled, regardless of direction. It is always positive.

  • Formula:

• Example: If a person walks from to , then and .

• Example (Negative Displacement): If a person walks from to , then and .

Vector Representation

• Displacement is represented as an arrow from the initial to the final position.

• Distance is the sum of the magnitudes of all path segments.

Average Speed and Velocity

Definitions

• Average Speed: The total distance traveled divided by the elapsed time.

  • Formula:

• Average Velocity: The displacement divided by the elapsed time. It is a vector and can be positive, negative, or zero.

  • Formula:

• Units: Both have units of length/time (e.g., m/s, km/h).

Example: Average Speed Calculation

• A car drives 4 miles at 30 mi/h, then 4 miles at 50 mi/h. The average speed is not simply the average of the two speeds, because the time spent at each speed is different.

• To find the average speed, calculate the total distance and total time, then divide.

Summary Table: Key Kinematic Quantities

Additional info: These notes cover the foundational concepts of 1D kinematics, including the importance of defining a coordinate system, distinguishing between displacement and distance, and calculating average speed and velocity. Further topics such as instantaneous velocity, acceleration, and motion with constant acceleration are typically covered in subsequent sections of a kinematics chapter.