Finding "change in motion" often refers to calculating displacement, which is the change in an object's position. Unlike distance, displacement is a vector quantity, meaning it has both size (magnitude) and direction.
Understanding Change in Position (Displacement)
Change in position, or displacement, tells you how far an object ended up from its starting point, in a specific direction. It's a fundamental concept in describing motion.
According to the reference, if an arrow is over the top of any value, it's a vector, meaning it has a size and a direction. This applies directly to displacement. For example, traveling 300 m in the positive direction describes a specific change in position as a vector quantity – 300 m is the size, and "positive direction" is the direction.
Calculating Displacement
The formula for calculating displacement is straightforward:
Δx = x_final - x_initial
Where:
- Δx represents the displacement (the change in position). The delta symbol (Δ) commonly means "change in".
- x_final is the object's final position.
- x_initial is the object's initial position.
Both initial and final positions are typically measured from a reference point (like the origin of a coordinate system).
Example Calculation
Imagine you start at a position of 10 meters from a reference point and move to a position of 50 meters.
- Initial position (x_initial) = 10 m
- Final position (x_final) = 50 m
Displacement (Δx) = x_final - x_initial = 50 m - 10 m = 40 m
Your change in position is 40 meters in the positive direction (assuming increasing position is positive).
What if you moved back to 5 meters from the starting point?
- Initial position (x_initial) = 10 m
- Final position (x_final) = 5 m
Displacement (Δx) = x_final - x_initial = 5 m - 10 m = -5 m
Your change in position is 5 meters in the negative direction. The negative sign indicates the direction relative to the chosen positive direction.
Key Differences: Displacement vs. Distance
It's crucial to distinguish displacement from distance traveled:
| Feature | Displacement | Distance Traveled |
|---|---|---|
| Type | Vector (size & direction) | Scalar (size only) |
| Definition | Change in position from start to end | Total path length covered |
| Formula | x_final - x_initial | Sum of lengths of path segments |
| Example | Moving 5m forward then 5m back = 0m displacement | Moving 5m forward then 5m back = 10m distance |
Understanding displacement as a vector, as highlighted in the reference, is key to describing change in position accurately.
While "change in motion" can also sometimes refer to concepts like change in velocity (acceleration) or change in momentum, calculating change in position (displacement) using the final and initial positions is a fundamental way to quantify how an object's location has changed.
