BackVectors, Scalars, Distance, and Displacement: Fundamental Concepts in Physics Measurement
Study Guide - Smart Notes
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Measurement in Physics
Magnitude and Direction in Measurements
In physics, measurements are used to quantify physical quantities. Every measurement has a magnitude (the size or amount), and some measurements also have a direction. The presence or absence of direction determines whether a quantity is classified as a vector or a scalar.
Magnitude: The numerical value representing the size of the measurement (e.g., 60°F, 10 kg).
Direction: Specifies the orientation of the measurement (e.g., 10m right, 20 miles/hr NORTH).
Vector: A quantity with both magnitude and direction.
Scalar: A quantity with magnitude only, no direction.
Measurements with direction are Vectors; those without direction are Scalars.
Classification of Common Physical Quantities
The following table summarizes the classification of various physical quantities as vectors or scalars, along with their properties:
Measurement | Quantity | Magnitude? | Direction? | Vector/Scalar |
|---|---|---|---|---|
"Apple weighs 5kg" | Mass | yes | x | Scalar |
"Days are 24hr long" | Time | yes | x | Scalar |
"It is 60°F outside" | Temperature | yes | x | Scalar |
"I pushed with 100N left" | Force | yes | yes | Vector |
"I walked 10 ft" | Distance | yes | x | Scalar |
"I walked 10 ft east" | Displacement | yes | yes | Vector |
"I drove at 80 mph" | Speed | yes | x | Scalar |
"I drove 80 mph west" | Velocity | yes | yes | Vector |
Distance and Displacement
Definitions and Differences
When measuring how far something moves, two related but distinct terms are used: distance and displacement.
Distance (d): The total length of the path traveled, regardless of direction. It is always positive and is a scalar quantity.
Displacement (Δx): The change in position from the initial to the final point, measured along the shortest path. It can be positive or negative, depending on direction, and is a vector quantity.
Formulas
Distance:
Displacement:
Examples and Applications
Consider a person walking along a straight path:
If the person walks 10m forward, then 6m backward, the distance traveled is m.
The displacement is m (net change in position).
Distance is always positive, while displacement can be negative, zero, or positive, depending on the direction of movement.
Worked Example
Situation | Initial Position () | Final Position () | Distance () | Displacement () |
|---|---|---|---|---|
A to B | -2 | 7 | 9 | 9 |
B to A | 6 | 0 | 6 | -6 |
A to B | 4 | 10 | 6 | 6 |
Additional info: In physics, the sign of displacement (+/-) is used to indicate direction, while distance is always a positive value.
Practice Problem
Application of Distance and Displacement
Suppose you walk so that your total distance traveled is 300m. What is the magnitude and direction of your total displacement?
Distance: m (total path length)
Displacement: The magnitude and direction depend on the starting and ending positions. If you return to your starting point, displacement is $0 m east.
Additional info: Displacement is a vector and requires both magnitude and direction for a complete description.
