Multi-Stage Displacement
Multi-Stage Displacement problems involve 3 or more movement segments in different directions. You must track cumulative net displacement to find the final position and straight-line distance from the starting point. These problems test systematic coordinate tracking and vector addition.
What You'll Learn
Introduction to Multi-Stage Displacement
Multi-Stage Displacement problems involve 3 or more movement segments in different directions. You must track cumulative net displacement to find the final position and straight-line distance from the starting point. These problems test systematic coordinate tracking and vector addition.
Prerequisites
How to Solve Multi-Stage Displacement Problems
Step 1: Start at origin (0,0)
Step 2: For each movement, update coordinates
Step 3: Track running total of x and y
Step 4: After all movements, net displacement = (x, y)
Step 5: Distance = √(x² + y²)
Step 6: Direction = determined by sign of x and y
Step 7: Answer with distance and direction if asked
Example Problem
Example: A person walks 10 m East, 5 m North, 3 m West, 8 m South. Find displacement. Solution: Step 1: Start (0,0) Step 2: 10 E → (10,0) Step 3: 5 N → (10,5) Step 4: 3 W → (7,5) Step 5: 8 S → (7,-3) Step 6: Net = (7,-3) Step 7: Distance = √(7² + 3²) = √58 ≈ 7.62 m Answer: 7.62 m
Pro Tips & Tricks
- Net x = Σ(East) - Σ(West)
- Net y = Σ(North) - Σ(South)
- Distance = √(x² + y²)
- Total path length = sum of all distances
- Displacement ≤ Total path length
- If net (x,y) = (0,0), person returns to start
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Multi-Stage Displacement. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Multi-Stage Displacement is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Multi-Stage Displacement?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: