Unit 1.3: Representing Motion

Introduction

Motion can be described using words, equations, diagrams, and graphs. Understanding different representations of motion allows us to analyze movement mathematically and conceptually. This section focuses on motion diagrams, graphs, and mathematical models.

Key Concepts

Motion Diagrams: A sequence of images representing an object's position at equal time intervals.
Position-Time Graphs: The slope of a position-time graph represents velocity.
Velocity-Time Graphs: The slope represents acceleration, and the area under the curve represents displacement.
Acceleration-Time Graphs: The area under an acceleration-time graph represents velocity change.
Particle Model: An object’s motion can be simplified by representing it as a single point moving through space.

Tip: Graphs provide information about motion even without numbers—focus on slopes and areas for qualitative analysis.

Motion Diagrams

A motion diagram shows an object's position at equal time intervals using dots. The spacing of dots indicates speed:

If dots are evenly spaced, the object is moving at constant velocity.
If dots get farther apart, the object is accelerating.
If dots get closer together, the object is decelerating.

Example:

A ball rolling down a ramp will have dots getting farther apart as it speeds up.

Graphical Representations

Graphs provide a powerful way to visualize motion. Each type of graph provides different information:

Position vs. Time Graph: The slope represents velocity.
Velocity vs. Time Graph: The slope represents acceleration, and the area represents displacement.
Acceleration vs. Time Graph: The area under the curve represents velocity change.

Example:

If a velocity-time graph shows a constant positive slope, the object is moving with constant acceleration.

Mathematical Routines

Understanding graphs involves interpreting slopes and areas:

Slope of a Position-Time Graph: \( v = \frac{\Delta x}{\Delta t} \)
Slope of a Velocity-Time Graph: \( a = \frac{\Delta v}{\Delta t} \)
Area Under a Velocity-Time Graph: \( \Delta x = v \cdot t \)

Tip: When analyzing graphs, look at both slopes and areas to determine motion characteristics.

Scientific Reasoning

Interpreting motion representations requires logical reasoning:

Question: "How can you determine acceleration from a velocity-time graph?"
Answer: The slope of a velocity-time graph tells us the acceleration value.
Question: "How does a position-time graph look for constant acceleration?"
Answer: It is a parabola because the position equation includes \( t^2 \).

Exam Strategy: Pay close attention to graph shapes and what they represent.

Practice Activities

Activity 1: Sketching Motion Diagrams

A car moves at constant speed for 3 seconds, then accelerates for 3 more seconds. Draw a motion diagram for this scenario.

Activity 2: Graph Matching

Match the following position-time graphs with the correct description:
(A) A stationary object
(B) A moving object with constant velocity
(C) An object accelerating

Activity 3: Velocity from Graphs

Given a position vs. time graph with a curved slope, determine whether the object is accelerating or decelerating.

Summary & Exam Preparation Tips

In this unit, we learned how motion can be represented using diagrams, graphs, and mathematical equations. Key takeaways:

Motion diagrams represent an object's position over time.
Graphs provide quantitative descriptions of motion.
The slope of a graph tells us the rate of change (velocity or acceleration).
The area under a velocity-time graph gives displacement.

Understanding these representations will be crucial for solving kinematics problems on the AP Physics exam.