Topic 1.1: Distance, Displacement, Vectors, and Scalars

Name: _______________________________ Date: _______________

Before We Start

Welcome to Unit 1! If you walked from your bed to the bathroom and back this morning, did you travel a distance? Did you end up anywhere different from where you started? Hold onto that thought.

Today's New Concepts

AP CED Alignment: Unit 1, Topics 1.1 and 1.2

Distance

Total length of the path actually traveled, start to finish — like a car's odometer, it just keeps adding up
No formula — add up each segment of the path
Always positive — no such thing as "negative distance"
A scalar quantity: size only, no direction

Displacement

Change in position, measured as a straight line from start to end — like a GPS pin, it only cares where you ended up
Symbol: $\Delta x = x - x_i$ (x = final position, xᵢ = initial position)
Sign matters: positive or negative depending on your chosen positive direction
A vector quantity: needs a size AND a direction to be complete

Scalar vs. Vector (the bigger picture)

Scalar = magnitude only. Examples: distance, speed, time, mass
Vector = magnitude + direction. Examples: displacement, velocity, acceleration, force
Leaving off the direction on a vector answer means the answer is incomplete, even if the number is right

Adding Vectors Along a Line (1D)

Same direction → add the magnitudes
Opposite directions → subtract the smaller from the larger; answer points in the direction of the larger one
Full 2D vector addition (angles) comes later in the unit

Worked Example: A student walks 50 m east, then 20 m west.

$\text{Distance} = 50 + 20 = 70\text{ m}$
$\text{Displacement} = 50 - 20 = 30\text{ m east}$ (opposite directions → subtract)

Keep This Sheet!

These sheets build into your semester study guide. Keep them in order in a binder or folder — you'll want to flip back through them before quizzes, unit tests, and when AP exam review starts in the spring.