Scalars and vectors in one dimension

Key Definition Every physical quantity in AP Physics is either a scalar (described by magnitude alone) or a vector (described by both magnitude and direction).

Scalars

• Distance
• Speed
• Mass
• Time

Vectors

• Position
• Displacement
• Velocity
• Acceleration
• Force

Vectors are represented as arrows whose length is proportional to magnitude and whose orientation shows direction. In one dimension, the sign of a component fully describes its direction, so arrow notation above the symbol is not required for components along an axis.

Adding vectors in one dimension

1. Choose a positive direction along the axis.
2. Assign each vector a signed component according to that chosen direction.
3. Sum the components algebraically to find the resultant.

A positive result points in the chosen positive direction; a negative result points in the opposite direction. This sign-based addition method underpins every one-dimensional problem in the course — from net force to net displacement to total momentum. Keeping the scalar–vector distinction sharp prevents errors that cost credit on both multiple-choice and free-response questions throughout the entire AP exam.

At a Glance