Overview
This lecture focuses on interpreting velocity-time graphs, highlighting the differences from displacement-time graphs, how to determine direction, acceleration, and how to calculate displacement and distance using the area under the graph.
Understanding Velocity-Time Graphs
- A velocity-time graph shows how an object's velocity changes over time.
- Positive velocity indicates movement in a defined positive direction (East); negative velocity means movement in the opposite direction (West).
- Steeper slopes represent faster acceleration; a horizontal line at zero means the object is stationary.
- Constant velocity appears as a horizontal (non-zero) line; changing velocity appears as a sloped line.
Interpreting Graph Features
- If the graph slopes upwards from left to right, the object is accelerating (speed increasing).
- If the graph slopes downwards but stays above zero, the object is decelerating but moving in the same direction.
- When the graph crosses the x-axis (velocity = 0), the object stops momentarily.
- Negative velocity values mean the object moves in the opposite direction; sloped lines below the x-axis show acceleration or deceleration in that direction.
- Area under the velocity-time graph represents displacement (can be positive or negative).
Calculating Acceleration and Displacement
- Acceleration is calculated as change in velocity divided by change in time: ( a = \frac{v_{final} - v_{initial}}{t_{final} - t_{initial}} ).
- Displacement is determined by finding the signed area between the graph and the time axis; positive area is one direction, negative is the opposite.
- Distance is the sum of absolute areas regardless of direction (no negatives).
- For triangles: Area = ½ × base × height. For rectangles: Area = base × height.
Practice Example Steps
- Identify intervals on the graph for velocity, acceleration, or area calculations.
- Assign directions based on sign (positive = East, negative = West).
- Always state direction for displacement (vector); no direction needed for distance (scalar).
- When calculating distance, ignore negative signs; for displacement, include them.
Key Terms & Definitions
- Velocity-Time Graph — A plot showing how velocity varies with time.
- Velocity — Speed with a specific direction.
- Acceleration — Change in velocity per unit time.
- Displacement — Change in position with direction (vector).
- Distance — Total path length traveled (scalar).
- Area Under the Curve — Gives displacement (keep signs) or distance (ignore signs).
Action Items / Next Steps
- Practice identifying acceleration, displacement, and distance for various velocity-time graphs.
- Memorize area formulas for triangles and rectangles for graph calculations.
- Review direction conventions (positive = East/right, negative = West/left).
- Watch the next video for additional practice questions.