Overview
This lecture explains the four equations of motion for objects moving with constant acceleration and demonstrates how to apply them to solve physics problems.
Introduction to Equations of Motion
- Equations of motion describe the movement of objects with constant acceleration.
- They connect four key quantities: velocity, acceleration, displacement, and time.
- These equations help calculate distance traveled, time taken, speed, or acceleration.
The Four Variables in Equations of Motion
- Each equation contains four variables (final velocity, initial velocity, acceleration, displacement, or time).
- VF (final velocity): Measured in meters/second (m/s).
- VI (initial velocity): Measured in meters/second (m/s).
- a (acceleration): Measured in meters/second squared (m/s²).
- Δx (displacement/distance/length): Measured in meters (m).
- For vertical motion, Δy replaces Δx to indicate change in the y-direction.
- t (time): Measured in seconds (s).
Scalars and Vectors
- Velocity, acceleration, and displacement are vector quantities (require direction).
- Speed and distance are scalars (no direction needed).
Steps for Solving Problems
- List all variables provided in the question.
- Choose the equation that includes three known variables and one unknown.
- Write the formula before substituting values.
- Substitute known values to solve for the unknown variable.
- Always include units and direction (for vectors) in the final answer.
Example Problem 1: Car Accelerating
- Given: VI = 5 m/s, a = 2 m/s², t = 3 s, unknown: distance (Δx).
- Use the equation Δx = VI·t + ½·a·t².
- Substitute values: Δx = 5·3 + ½·2·(3)² = 24 m.
- Since distance is a scalar, only the unit (m) is needed.
Example Problem 2: Rocket Powered Sled
- Given: VF = 444 m/s, VI = 0 m/s (from rest), t = 1.8 s.
- To find acceleration: Use a = (VF - VI)/t → a = (444 - 0)/1.8 = 246.67 m/s² (needs direction).
- To find distance: Use Δx = ½(VI + VF)t → Δx = ½(0 + 444)·1.8 = 399.6 m.
Key Terms & Definitions
- Velocity (v): Speed with direction, vector quantity, measured in m/s.
- Acceleration (a): Rate of change of velocity, vector, m/s².
- Displacement (Δx/Δy): Change in position, vector, m.
- Speed: Scalar, magnitude of velocity, m/s.
- Distance: Scalar, path length traveled, m.
- Time (t): Duration of motion, scalar, s.
Action Items / Next Steps
- Practice more equations of motion problems with different variables.
- Review the next video or reading for additional practice questions.
- Always write the formula, substitutions, and answer with proper units and direction.