BackKinematics in One Dimension: Position, Velocity, and Acceleration
Study Guide - Smart Notes
Tailored notes based on your materials, expanded with key definitions, examples, and context.
Kinematics in One Dimension
Introduction
Kinematics is the branch of physics that describes the motion of objects without considering the causes of motion. In one-dimensional kinematics, we analyze motion along a straight line, focusing on key quantities such as position, velocity, and acceleration.
Key Concepts in One-Dimensional Motion
Essential Questions
Where is it? → Position
How fast is it moving and in which direction? → Velocity
How do speed and direction of motion change? → Acceleration
Position
Definition and Representation
The position of an object is its location relative to a chosen reference point (origin) in a coordinate system. It is typically denoted by the variable x in one dimension.
Numerical value: The position is given as a number (with units, usually meters) along a straight line.
Position as a function of time: describes how the position changes over time.
Initial position: , where is the initial time. Note: does not have to be zero.
Example: If a person stands at m at s, their initial position is m.
Coordinate Systems
Reference Frames
A coordinate system is used to specify the position of objects. In one dimension, this is usually a straight line (the x-axis), but in general, a two-dimensional (x, y) system can be used for more complex motion.
Origin (O): The reference point where (and in 2D).
Points: Each point is specified by its coordinates, e.g., or .
Example: On a number line, a tree at m and a person at m are located relative to the origin.
Speed and Velocity
Definitions
Speed: The rate at which an object covers distance, regardless of direction. It is a scalar quantity.
Velocity: The rate at which an object changes its position, including direction. It is a vector quantity.
Instantaneous speed is the speed at a specific moment in time. Instantaneous velocity includes both speed and direction at that instant.
Example: "I am currently going at 25 mph" (speed only).
Example: "I am currently going at 25 mph north on Madison Ave" (velocity: speed and direction).
Direction of Velocity
If , the object moves in the positive x-direction.
If , the object moves in the negative x-direction.
Example: A car moving to the right (positive x-direction) has ; to the left (negative x-direction), .
Displacement
Definition and Properties
Displacement is a vector that points from an object's initial position to its final position. It measures the change in position, not the total distance traveled.
Formula:
Unit: meter (m)
Sign convention: Displacement in one direction is positive; in the opposite direction, it is negative.
Example: If a car moves from m to m, m.
Average Velocity
Definition and Formula
Average velocity is the displacement divided by the elapsed time.
Formula:
Unit: meters per second (m/s)
Example: If a runner moves 100 m in 10 s, .
Summary Table: Key Kinematic Quantities
Quantity | Symbol | Definition | Unit |
|---|---|---|---|
Position | Location relative to origin | meter (m) | |
Displacement | Change in position: | meter (m) | |
Speed | Distance per unit time (no direction) | m/s | |
Velocity | Displacement per unit time (with direction) | m/s |
Additional info: Acceleration, kinematic equations, and graphical analysis are also essential in one-dimensional kinematics, but are not fully covered in the provided images. For completeness, students should study how acceleration describes changes in velocity and how to use kinematic equations for constant acceleration.
