Overview
This lecture explains how to interpret position, velocity, and acceleration motion graphs, focusing on slopes and areas to analyze an object's movement.
Motion Graphs Overview
- Motion graphs represent an object’s movement using position, velocity, or acceleration versus time.
- Different graphs reveal different aspects: position shows location, velocity shows speed and direction, acceleration shows rate of velocity change.
Position vs. Time ((x) vs. (t)) Graphs
- Slope of the graph gives velocity; greater slope means faster movement.
- Constant positive slope: constant positive velocity (no acceleration).
- Zero slope: no movement (velocity and acceleration are zero).
- Increasing slope: increasing velocity, indicating acceleration.
- Constant negative slope: constant negative velocity (no acceleration).
- Decreasing (negative) slope: object slows down; acceleration is in the opposite direction of motion.
- Derivative of position vs. time graph gives velocity.
Velocity vs. Time ((v) vs. (t)) Graphs
- Instantaneous velocity shown by the graph’s value at each moment.
- Slope indicates acceleration; constant slope means constant acceleration.
- Area under the curve represents total displacement.
- Flat positive line: constant positive velocity (no acceleration).
- Decreasing line: object slowing down (negative acceleration).
- Crosses the time axis: change in direction.
- Increasing slope: increasing acceleration.
- Derivative of velocity vs. time graph gives acceleration; integral gives displacement.
Acceleration vs. Time ((a) vs. (t)) Graphs
- Typically show constant positive, constant negative, or zero acceleration.
- Flat line above zero: constant positive acceleration.
- Flat line below zero: constant negative acceleration.
- Area under the curve gives the change in velocity over that time interval.
Key Terms & Definitions
- Position ((x)) — the location of an object at a certain time.
- Velocity ((v)) — rate of change of position; slope of position vs. time.
- Acceleration ((a)) — rate of change of velocity; slope of velocity vs. time.
- Slope — in these graphs, represents rate of change (derivative).
- Area under curve — in velocity vs. time, gives displacement; in acceleration vs. time, gives change in velocity.
- Displacement — overall change in position.
Action Items / Next Steps
- Practice interpreting position, velocity, and acceleration graphs.
- Review calculus concepts: derivatives (slopes) and integrals (areas) as they apply to motion graphs.