Displacement Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
A particle undergoes three displacements: d1⃗=(2,−1)\vec{d_1} = (2, -1), d2⃗=(−3,4)\vec{d_2} = (-3, 4), d3⃗=(1,2)\vec{d_3} = (1, 2). Find the net displacement vector and its magnitude.

Solution

  1. 1
    Step 1: Net displacement =d1⃗+d2⃗+d3⃗=(2−3+1, −1+4+2)=(0,5)= \vec{d_1} + \vec{d_2} + \vec{d_3} = (2-3+1,\ -1+4+2) = (0, 5).
  2. 2
    Step 2: Starting at origin (0,0)(0,0): after all three moves the particle is at (0,5)(0, 5).
  3. 3
    Step 3: Magnitude =02+52=5= \sqrt{0^2+5^2} = 5 units.

Answer

Net displacement =(0,5)= (0, 5), magnitude =5= 5 units (due north).
Vector addition is the key: displacements add component-wise. The net displacement is path-independent — it only depends on the starting and ending positions. This is the fundamental property that makes displacement a vector quantity.

About Displacement

The straight-line change in position from start to end, with both a distance and a direction.

Learn more about Displacement →

More Displacement Examples

Example 1 easy

A person walks 5 m east and then 5 m west. What is their displacement?

Example 2 medium

A robot moves from point [formula] to point [formula]. Find the displacement vector and its magnitud

Example 3 easy

A car drives 3 km north, then 4 km east. What is the magnitude of the total displacement?

← All Displacement Examples Displacement Concept