Unit 1 · 1.1 — Scalars and Vectors in One Dimension

Everything to learn here

• Concept: Physical quantities in kinematics are classified as either scalars (magnitude only) or vectors (magnitude and direction)
• Concept: A reference frame and coordinate system must be established to define positive and negative directions for one-dimensional analysis
• Concept: In one-dimensional kinematics, the direction of a vector is exclusively indicated by a positive or negative sign relative to a user-defined coordinate axis
• Concept: Comparisons of scalar quantities evaluate magnitude only, whereas comparisons of vector quantities must evaluate both magnitude and direction
• Equation: $$d=\sum |\Delta x|\text{(Distance calculation)}$$
• Equation: $$\Delta x=x_f-x_i\text{(Displacement calculation)}$$
• Vocabulary: Scalar — A physical quantity described strictly by a magnitude and a unit (e.g., time, mass, distance, speed)
• Vocabulary: Vector — A physical quantity described by both a magnitude and a direction (e.g., position, displacement, velocity, acceleration)
• Vocabulary: Position (x) — The location of an object at a given moment relative to a defined origin
• Vocabulary: Distance — The total scalar path length traveled by an object, regardless of direction
• Vocabulary: Displacement — A vector representing the straight-line change in position from the initial point to the final point
• Skill: Translation Between Representations — Drawing proportional vector arrows to represent the magnitude and direction of displacement
• Skill: Science Practice 2.C — Compare physical quantities between two or more scenarios, requiring the identification of both numerical magnitude and directional sign
• Skill: Creating Representations — Translate a verbal description of one-dimensional motion into a number-line diagram that preserves scale and directional signs
• Concept: A vector sum in one dimension is computed by adding signed quantities — opposite directions are denoted by opposite signs in a chosen coordinate system
• Skill: Mathematical Routines — Determine a one-dimensional vector sum by assigning positive and negative signs to opposite directions and adding the magnitudes algebraically
• Skill: Calculate the resultant of one-dimensional vectors by summing magnitudes while accounting for direction via positive and negative signs.
• Vocabulary: Vocabulary: Scalars and Vectors — Scalars have only magnitude, whereas vectors possess both magnitude and direction, often denoted with an arrow symbol.
• Concept: In a 1D coordinate system, opposite directions are represented by opposite signs to allow for algebraic vector addition.

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