Overview
This lecture explains the concept of acceleration, how to calculate it, how to use velocity-time graphs, and how to determine distance traveled for both constant and non-constant acceleration.
Acceleration Basics
- Velocity is defined as speed in a given direction and is a vector quantity.
- Acceleration measures the change in velocity over a given time.
- Acceleration equation: acceleration (m/s²) = change in velocity (m/s) ÷ time (s).
- You must memorize the acceleration equation for exams.
Example Calculations
- Example 1: A car's velocity increases from 15 m/s to 35 m/s in 20 s, so acceleration = (35-15)/20 = 1 m/s².
- Example 2: A cyclist slows from 6 m/s to 0 m/s in 12 s, so acceleration = (0-6)/12 = -0.5 m/s².
- Negative acceleration indicates deceleration (object slowing down).
Velocity-Time Graphs
- Velocity-time graphs may be required in exams.
- The gradient (slope) of a velocity-time graph gives the object's acceleration.
- A horizontal line indicates constant velocity.
- Upward sloping line = acceleration; downward sloping line = deceleration.
- Acceleration from graph: (final velocity – initial velocity) ÷ time interval.
Higher Tier: Calculating Distance from Graphs
- The area under a velocity-time graph represents distance traveled (displacement).
- For constant acceleration, break the area under the graph into simple shapes (triangles, rectangles), calculate each, and sum them.
- If the shape is irregular (acceleration not constant), count the complete and partial squares under the graph, multiply by area per square to estimate total distance.
Key Terms & Definitions
- Velocity — Speed in a specific direction; a vector quantity.
- Acceleration — Change in velocity divided by time; measured in m/s².
- Deceleration — Negative acceleration; the object is slowing down.
- Displacement — Distance traveled in a specific direction; area under a velocity-time graph.
Action Items / Next Steps
- Memorize the acceleration formula.
- Practice calculating acceleration and displacement from sample problems and velocity-time graphs.
- Complete workbook questions on acceleration and velocity-time graphs if assigned.