Overview
This lecture explains the four equations of motion used to describe an object's movement with constant acceleration, including how to choose and apply the correct formula to solve physics problems.
Introduction to Equations of Motion
- Equations of motion let us calculate distance, time, speed, and acceleration for moving objects with constant acceleration.
- Four key variables are used: initial velocity (VI), final velocity (VF), acceleration (a), and displacement (Δx or distance).
- Each equation relates four variables, so you should know three to solve for the fourth.
Variables, Units, and Vectors
- VF: final velocity or speed, measured in meters/second (m/s).
- VI: initial velocity or speed, measured in meters/second (m/s).
- a: acceleration, measured in meters/second squared (m/s²), indicates speeding up or slowing down.
- Δx: displacement or distance (horizontal movement) in meters (m); use Δy for vertical movement.
- t: time, measured in seconds (s).
- Velocity, acceleration, and displacement are vectors (require direction); speed and distance are scalars (no direction needed).
Steps to Solve Equations of Motion Problems
- List all known and unknown variables from the problem statement.
- Choose the equation that includes your three knowns and one unknown variable.
- Write the chosen formula before substituting values.
- Substitute values, solve for the unknown, include units, and add direction if it’s a vector.
Example 1: Car Acceleration
- Given: VI = 5 m/s, a = 2 m/s², t = 3 s; Find: distance (Δx).
- Use: Δx = VI×t + ½a×t².
- Substitute and solve: Δx = 5×3 + 0.5×2×3² = 15 + 9 = 24 m.
- Final answer: 24 m (distance, so no direction needed).
Example 2: Rocket Powered Sled
- Given: VF = 444 m/s, VI = 0, t = 1.8 s.
- Find acceleration: a = (VF - VI)/t = (444-0)/1.8 = 246.67 m/s² (needs direction).
- Find distance without using a: Δx = [(VI + VF)/2] × t = (0+444)/2 × 1.8 = 222×1.8 = 399.6 m.
Key Terms & Definitions
- Equations of Motion — Formulas connecting displacement, velocity, acceleration, and time for constant acceleration.
- Displacement (Δx or Δy) — Change in position (vector); Δx for horizontal, Δy for vertical.
- Velocity (VI, VF) — Speed with direction (vector).
- Acceleration (a) — Change in velocity over time (vector).
- Time (t) — Duration of motion in seconds.
Action Items / Next Steps
- Practice identifying variables and selecting equations using additional problem sets.
- Review units and remember when to include direction (for vectors).
- Watch the next video for more equation of motion practice questions.