How do you calculate displacement?

Displacement is calculated by subtracting the initial position from the final position. It's a vector quantity, meaning it has both magnitude (size) and direction.

Here's a breakdown:

Understanding Displacement

• Definition: Displacement is the shortest distance between the object's initial and final positions, along with the direction.
• Difference from Distance: Distance is the total length of the path traveled by an object, regardless of direction. Displacement only cares about the start and end points.
• Vector Quantity: Because displacement has both magnitude and direction, it's a vector. For example, "5 meters east" is a displacement.

Calculating Displacement

The formula for calculating displacement is:

Δx = x_f - x_i

Where:

• Δx represents displacement (often read as "delta x")
• x_f represents the final position
• x_i represents the initial position

Steps:

1. Identify the Initial Position (x_i): Determine the object's starting point.
2. Identify the Final Position (x_f): Determine the object's ending point.
3. Subtract Initial from Final: Calculate x_f - x_i. The result is the displacement, including its magnitude and direction (positive or negative in one-dimensional motion).

Examples

• Example 1: One-Dimensional Motion

  • A person starts at a position of 2 meters and walks to a position of 7 meters.
  • x_i = 2 meters
  • x_f = 7 meters
  • Δx = 7 meters - 2 meters = 5 meters
  • The displacement is 5 meters (in the positive direction).

• Example 2: Motion with Direction Change (One-Dimensional)

  • A car starts at x=0 meters, travels to x=10 meters, then back to x=5 meters.
  • x_i = 0 meters
  • x_f = 5 meters
  • Δx = 5 meters - 0 meters = 5 meters
  • The displacement is 5 meters from the starting point. The total distance traveled, however, would be 15 meters.

• Example 3: Two-Dimensional Motion (Requires Vector Components) Imagine a car travels 3 meters east and then 4 meters north. To find the displacement, you'd use the Pythagorean theorem:

  • Displacement = √(3² + 4²) = √(9 + 16) = √25 = 5 meters
  • The direction could be specified as an angle relative to the east (using trigonometry). tan^-1(4/3) ≈ 53.1 degrees north of east. So the displacement is 5 meters at 53.1 degrees north of east.

Importance of Displacement

Displacement is crucial in physics because it's used to calculate other important quantities, such as:

• Velocity: Velocity is displacement divided by time (velocity = displacement / time). This is different from speed, which is distance divided by time. Velocity is a vector, while speed is a scalar.
• Acceleration: Acceleration involves the change in velocity, which depends on displacement.