Overview
This lecture explains the interpretation of motion graphs in physics, including position-time, velocity-time, and acceleration-time graphs, focusing on the meaning of slope and area for each.
Slope & Area Concepts
- Slope is calculated by dividing change in y by change in x; it represents a rate (division).
- Area under a graph is found by multiplying y by x; it represents a quantity (multiplication).
- On a graph, slope = (y2 - y1)/(x2 - x1); area = length × width for rectangles.
Position-Time Graphs (x vs. t)
- Slope represents velocity (instantaneous if a tangent, average if a secant).
- Area under a position-time graph is not meaningful in physics.
- Positive slope: object moves right; negative slope: object moves left; zero slope: object at rest or changing direction.
Velocity-Time Graphs (v vs. t)
- Slope represents acceleration.
- Area under the curve gives displacement (change in position).
- Displacement = area under v-t graph = final position minus initial position.
Acceleration-Time Graphs (a vs. t)
- Slope is called "jerk" (rarely tested in basic physics).
- Area under the curve gives change in velocity (v_final - v_initial).
Tangent & Secant Lines
- Slope of a tangent line on a position-time graph gives instantaneous velocity.
- Slope of a secant line gives average velocity between two points.
- The closer the secant points, the better the estimation of instantaneous velocity.
Position vs. Distance-Time Graphs
- Slope of a position-time graph gives velocity (vector, can be negative).
- Slope of a distance-time graph gives speed (scalar, always positive).
- Velocity = displacement/time; Speed = distance/time.
Velocity, Speed & Acceleration
- Velocity is the rate of change of position; acceleration is the rate of change of velocity.
- Positive acceleration increases velocity; negative acceleration decreases velocity; zero acceleration: constant velocity.
- Speed = absolute value of velocity (always positive).
Speeding Up vs. Slowing Down
- Object speeds up if acceleration and velocity have the same sign.
- Object slows down if acceleration and velocity have opposite signs.
Fundamental Graph Shapes
- Linear increasing: velocity positive, acceleration zero.
- Linear decreasing: velocity negative, acceleration zero.
- Horizontal: velocity zero, acceleration zero.
- Parabolic/curved shapes: concave down = negative acceleration; concave up = positive acceleration.
Key Terms & Definitions
- Slope — Rate of change between two variables (division).
- Area under graph — Total quantity related to multiplication of axes values.
- Position-Time Graph — Plots position (x) versus time (t).
- Velocity-Time Graph — Plots velocity (v) versus time (t).
- Acceleration-Time Graph — Plots acceleration (a) versus time (t).
- Tangent Line — Touches a curve at one point, gives instantaneous rate.
- Secant Line — Connects two points on a curve, gives average rate.
- Jerk — Rate of change of acceleration.
Action Items / Next Steps
- Review examples of motion graphs and practice calculating slope and area.
- Memorize what slope and area represent for each type of graph.
- Complete any assigned problems related to motion graphs.