Overview
This lecture covers motion graphs, focusing on interpreting the slope and area of position-time, velocity-time, and acceleration-time graphs, and how these relate to physical quantities like velocity, acceleration, and displacement.
Slope and Area Concepts
- Slope represents division and is calculated as the change in y divided by the change in x.
- Area represents multiplication and is found by multiplying the y-value by the x-value.
Types of Motion Graphs
- Position-time graph (x vs. t or y vs. t) tracks motion along an axis.
- Velocity-time graph (v vs. t) represents velocity changes over time.
- Acceleration-time graph (a vs. t) shows acceleration over time.
Interpreting Slope and Area
- Slope of a position-time graph gives velocity (instantaneous if tangent, average if secant).
- Area under a position-time graph has no useful interpretation in basic physics.
- Slope of a velocity-time graph gives acceleration.
- Area under a velocity-time graph gives displacement.
- Slope of an acceleration-time graph gives jerk (rarely tested).
- Area under an acceleration-time graph gives change in velocity.
Position vs. Distance Graphs
- Slope of a position-time graph gives velocity (can be positive or negative).
- Slope of a distance-time graph gives speed (always positive, scalar).
Analyzing Graph Shapes
- Linear position-time graphs: constant velocity, zero acceleration.
- Increasing line: positive velocity.
- Decreasing line: negative velocity.
- Horizontal line: zero velocity (at rest or changing direction).
- Parabolic position-time graphs: changing velocity (acceleration present).
- Concave down: negative acceleration.
- Concave up: positive acceleration.
- Acceleration is negative when slope decreases, positive when slope increases.
Speeding Up vs. Slowing Down
- Object speeds up when velocity and acceleration have the same sign.
- Object slows down when velocity and acceleration have opposite signs.
Key Terms & Definitions
- Slope — Change in y divided by change in x; gives rate of change.
- Area — Multiplying y-value by x-value under a curve; gives cumulative quantity.
- Displacement — Change in position (final minus initial position), can be negative.
- Velocity — Rate of change of position; vector quantity.
- Speed — Absolute value of velocity; scalar quantity.
- Acceleration — Rate of change of velocity.
- Jerk — Rate of change of acceleration.
Action Items / Next Steps
- Review provided equations and definitions.
- Practice identifying slope and area meanings on sample motion graphs.
- Prepare notes for interpreting graph shapes and determining motion behaviors.