Overview
This lecture covers acceleration and the three constant acceleration motion equations (CAM eqs), and explains how to determine if an object is speeding up or slowing down.
Acceleration Basics
- Acceleration is the rate of change of velocity per unit time.
- Acceleration is a vector with units of meters per second squared (m/sĀ²).
- The basic equation for acceleration is ( a = \Delta v / t ), where (\Delta v) is change in velocity.
Constant Acceleration Motion Equations (CAM eqs)
- These equations apply when acceleration is constant (not changing over time).
1. Position (No V) Equation
- ( x = x_0 + v_0 t + \frac{1}{2} a t^2 )
- Use when final velocity is not given or needed.
- ( x ): final position; ( x_0 ): initial position; ( v_0 ): initial velocity; ( a ): acceleration; ( t ): time.
2. No Time (No t) Equation
- ( v^2 = v_0^2 + 2a\Delta x )
- Use when time is not given or needed.
- ( v ): final velocity; ( v_0 ): initial velocity; ( a ): acceleration; ( \Delta x ): change in position.
3. Velocity (No x) Equation
- ( v = v_0 + at )
- Use when position or displacement is not given or needed.
- Simplest equation for finding initial or final velocity.
Speeding Up vs. Slowing Down
- Object speeds up if acceleration and velocity have the same sign/direction (both positive or both negative).
- Object slows down if acceleration and velocity have opposite signs/directions.
- Negative acceleration does not always mean slowing down; direction matters.
Key Terms & Definitions
- Acceleration ā Rate at which velocity changes over time; a vector quantity.
- Velocity ā Speed with a direction; a vector.
- Constant Acceleration ā Acceleration that remains the same over time.
Action Items / Next Steps
- Review and memorize the three CAM eqs.
- Practice identifying when to use each equation based on problem information.
- Be able to determine if an object is speeding up or slowing down using the signs of velocity and acceleration.