Overview
This section introduces the concept of displacement in physics, distinguishing it from position, distance, and distance traveled, and explains how to calculate and interpret displacement in one-dimensional motion.
Position and Reference Frames
- Position describes where an object is at any particular time, relative to a chosen reference frame.
- Earth is commonly used as a reference frame, but other moving frames (like an airplane) can also be used.
- The choice of reference frame affects how motion and position are described.
Displacement
- Displacement is the change in position of an object.
- It is calculated as: displacement (Δx) = final position (xf) – initial position (x0).
- Displacement has both magnitude and direction (it is a vector).
- In one-dimensional motion, direction is indicated with a plus (positive) or minus (negative) sign based on the chosen coordinate system.
Examples of Displacement
- If a professor moves from 1.5 m to 3.5 m (to the right), her displacement is +2.0 m.
- If a passenger moves from 6.0 m to 2.0 m (to the rear), their displacement is –4.0 m.
Distance vs. Displacement
- Distance is the magnitude (size) of the displacement between two points, without considering direction.
- Distance traveled is the total path length taken, regardless of direction.
- The magnitude of displacement can be less than or equal to, but never greater than, the distance traveled.
Calculation Example
- A cyclist rides 3 km west then 2 km east:
- (a) Displacement = –1 km (west taken as negative)
- (b) Distance traveled = 5 km (3 km + 2 km)
- (c) Magnitude of displacement = 1 km
Key Terms & Definitions
- Position — The location of an object relative to a reference frame.
- Reference Frame — The perspective from which motion is observed and measured.
- Displacement (Δx) — The change in position of an object; Δx = xf – x0 (vector quantity).
- Distance — The magnitude of displacement between two positions.
- Distance Traveled — The total length of the path taken between two positions, regardless of direction (scalar).
Action Items / Next Steps
- Practice calculating displacement and distance for various motion scenarios.
- Read Section 2.2 on Vectors, Scalars, and Coordinate Systems.