Lecture Notes: Motion and Velocity

Key Concepts

Velocity: A vector quantity that indicates the speed of an object and its direction.
Constant Velocity: When an object moves at a consistent speed in a consistent direction.

Plotting the magnitude of velocity against time can help visualize an object's motion.
Constant Velocity Example:
- If an object moves with a constant velocity of 5 meters per second, its velocity is unchanging over time.
- After 5 seconds, the object will have traveled 25 meters. This can be calculated using the formula:
  - Velocity = Displacement / Time
  - Displacement = Velocity × Time = 5 m/s × 5 s = 25 meters
Area Under the Graph: Represents the displacement. For a rectangle, this is simply height (velocity) × width (time).

Constant Acceleration: When an object's velocity changes at a consistent rate.
Example of Constant Acceleration:
- Given acceleration is 1 meter per second squared.
- Initial velocity is 0.
Velocity-Time Graph for Acceleration:
- The slope of the line represents acceleration. A constant slope indicates constant acceleration.
- After 5 seconds at 1 m/s² starting from zero velocity, the velocity is 5 m/s.

With changing velocity, the displacement can be calculated as the area under the velocity-time graph.
For constant acceleration, the graph is a triangle:
- Area of Triangle = 1/2 × Base × Height
- For 5 seconds of acceleration from 0 to 5 m/s:
  - Base = 5 seconds
  - Height = 5 m/s
  - Area = 1/2 × 5 s × 5 m/s = 12.5 meters

Area Under the Curve: Provides the distance traveled over a period.
Slope of the Line: Indicates the acceleration. A flat line (zero slope) means constant velocity.
Even with constant acceleration, you can use the area under the curve to calculate distance.

Average Velocity: Introduction to average velocity and its calculation from velocity-time graphs will be covered in the next session.