1.1 Scalars and Vectors in One Dimension

Learning objectives

1.1A—Describe a scalar or vector quantity using magnitude and direction, as appropriateDescribe a scalar or vector quantity using magnitude and direction, as appropriate.• Scalars are quantities described by magnitude only; vectors are quantities described by both magnitude and direction.• Vectors can be visually modeled as arrows with appropriate direction and lengths proportional to their magnitude.• Distance and speed are examples of scalar quantities, while position, displacement, velocity, and acceleration are examples of vector quantities.- i. Vectors are notated with an arrow above the symbol for that quantity. Relevant equation: = +  vv at0- ii. 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. Derived equation: =+vv atxx x0 TOPIC 1.1 Scalars and Vectors in One Dimension 1.1B—Describe a vector sum in one dimensionDescribe a vector sum in one dimension.• When determining a vector sum in a given one-dimensional coordinate system, opposite directions are denoted by opposite signs. AP Physics 1: Algebra-Based Course and Exam Description Kinematics UNIT 1

A scalar answers ‘how much?’ A vector answers ‘how much and in which direction?’

Quantity	Type	What must be specified
Distance	Scalar	Magnitude only
Speed	Scalar	Magnitude only
Position	Vector	Location relative to an origin, including direction
Displacement	Vector	Change in position, including direction
Velocity	Vector	Rate of change of position, including direction
Acceleration	Vector	Rate of change of velocity, including direction

In one dimension, a sign can encode direction only after a positive axis has been chosen. A negative component means ‘opposite the positive direction’—not ‘slower’ or ‘smaller.’

Set the direction convention

Choose one positive direction. Write vectors in that direction as positive and vectors in the opposite direction as negative, then add their one-dimensional components.

Add the signed components

$\Delta x_{\text{net}}=(+5\,\mathrm{m})+(-2\,\mathrm{m})=+3\,\mathrm{m}$

For this hypothetical motion, take right as positive: a 5 m displacement to the right is $+5\,\mathrm{m}$ and a 2 m displacement to the left is $-2\,\mathrm{m}$ . The resultant is $+3\,\mathrm{m}$ , so its magnitude is 3 m and its direction is right.

Interpret the sign

The sign of the answer depends on the chosen axis; the physical resultant does not. Choosing left as positive would give $-3\,\mathrm{m}$ , which still describes 3 m to the right.

Next Topic

—1.2 Displacement, Velocity, and AccelerationRead