Scalars and Vectors in One Dimension

AP Topic 1.1

Hercules the Archer, Antoine Bourdelle, 1909

Learning Objectives

• Describe a scalar or vector quantity using magnitude and direction, as appropriate.
• Describe a vector sum in one dimension.

Scalars vs. Vectors

• Scalars are quantities described by magnitude only
• Examples: distance (d) and speed (s)
• Vectors are quantities described by both magnitude and direction.
• Examples: position (x), displacement (Δx), velocity (v), and acceleration (a)

Visualization of Vectors

Vectors can be visually modeled as arrows with appropriate direction and lengths proportional to their magnitude.

Vectors with the same magnitude but opposite direction are shown with a positive sign in one direction and a negative sign in the other.

Vector Notation

• Vectors are notated with an arrow above the symbol for that quantity.
• Examples: Δx, v, and a
• Vector notation is not required for vector components along an axis. In one dimension, the sign of the component completely describes the direction of that component.
• Examples: +v_x vs –v_x and +a_x and –a_x

Adding Vectors in 1D

When determining a vector sum in a given one-dimensional coordinate system, opposite directions are denoted by opposite signs.

Adding Vectors in 1D

When determining a vector sum in a given one-dimensional coordinate system, opposite directions are denoted by opposite signs.

Adding Vectors in 1D

When determining a vector sum in a given one-dimensional coordinate system, opposite directions are denoted by opposite signs.

Adding Vectors in 1D

When determining a vector sum in a given one-dimensional coordinate system, opposite directions are denoted by opposite signs.

Adding Vectors in 1D

When determining a vector sum in a given one-dimensional coordinate system, opposite directions are denoted by opposite signs.

Adding Vectors in 1D

When determining a vector sum in a given one-dimensional coordinate system, opposite directions are denoted by opposite signs.

Adding Vectors in 1D

When determining a vector sum in a given one-dimensional coordinate system, opposite directions are denoted by opposite signs.

Adding Vectors in 1D

When determining a vector sum in a given one-dimensional coordinate system, opposite directions are denoted by opposite signs.

Adding Vectors in 1D

When determining a vector sum in a given one-dimensional coordinate system, opposite directions are denoted by opposite signs.

Adding Vectors in 1D

When determining a vector sum in a given one-dimensional coordinate system, opposite directions are denoted by opposite signs.

Adding Vectors in 1D

When determining a vector sum in a given one-dimensional coordinate system, opposite directions are denoted by opposite signs.

Adding Vectors in 1D

When determining a vector sum in a given one-dimensional coordinate system, opposite directions are denoted by opposite signs.