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.

10Worksheets
200+Practice Questions
HardDifficulty
2-3 hoursHours to Master

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

Coordinate geometry Net displacement concept Vector addition Pythagorean theorem
Why This Matters: Multi-Stage Displacement problems appear in 1-2 questions in advanced exams. They test complex path analysis and net displacement calculation.

How to Solve Multi-Stage Displacement Problems

1

Step 1: Start at origin (0,0)

2

Step 2: For each movement, update coordinates

3

Step 3: Track running total of x and y

4

Step 4: After all movements, net displacement = (x, y)

5

Step 5: Distance = √(x² + y²)

6

Step 6: Direction = determined by sign of x and y

7

Step 7: Answer with distance and direction if asked

Pro Strategy: Keep running totals of x (East-West) and y (North-South) coordinates. The order of movements doesn't matter for net displacement, but sequential tracking helps avoid errors.

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

Calculate net x and net y separately
Use Pythagorean theorem for final distance
Direction: if x>0,y>0 → NE; x>0,y<0 → SE; etc.

Common Mistakes to Avoid

Adding distances instead of net displacement
Mixing up x and y coordinates
Forgetting to use signs for opposite directions

Exam Importance

Multi-Stage Displacement is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
1-2 questions
BANKING PO
1-2 questions
RAILWAYS RRB
1-2 questions
CAT
1-2 questions
INSURANCE
1-2 questions

Ready to Master Multi-Stage Displacement?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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