Topic 1.2: Average Velocity, Average Speed, and Intro to Acceleration

Name: _______________________________ Date: _______________

Before We Start: Yesterday's Recap

Yesterday we learned vectors vs. scalars. Without looking back: sort these into vector or scalar — time, velocity, mass, displacement.

Today's New Concepts

AP CED Alignment: Unit 1, Topic 1.2 (Displacement, Velocity, and Acceleration)

Average Velocity

How fast AND in what direction an object's position changed overall, from the start to the end of a time interval
A vector quantity — built from displacement, not total distance
Formula: $v_{avg} = \dfrac{\Delta x}{\Delta t}$ (displacement divided by time interval)
Units: meters per second (m/s)
Sign/direction matters — a negative value just means motion in the direction you defined as negative

Average Speed

How much ground an object covered overall, with no regard for direction
A scalar quantity — built from total distance, not displacement
Formula: $\text{speed}_{avg} = \dfrac{\text{total distance}}{\text{total time}}$
Units: meters per second (m/s)
Always positive — speed never reports a direction

Why They Can Give Different Answers

Average velocity only "sees" the net change in position (start to end)
Average speed adds up every bit of ground covered, including backtracking
They match exactly only when motion is in a single direction the whole time, with no reversals

Worked Example: A cyclist rides 8 km east in 20 minutes, then 8 km west in 20 minutes (ending back where they started).

$\text{Average speed} = \dfrac{16\text{ km}}{40\text{ min}} \approx 24\text{ km/h}$
$\text{Average velocity} = \dfrac{0\text{ km}}{40\text{ min}} = 0$ (they ended up right where they began)

Acceleration (preview — full lesson in Topic 1.2, Session 4)

The rate at which velocity itself is changing, over time
A vector quantity — built from a change in velocity, not velocity itself
Formula (preview only, we'll practice this in Topic 1.2, Session 4): $a = \dfrac{\Delta v}{\Delta t}$ (change in velocity divided by time interval)
Units: meters per second, per second (m/s²) — a unit that looks strange until Topic 1.2, Session 4 when we work through why
Key idea to hold onto: speeding up, slowing down, AND changing direction are all forms of acceleration — "accelerating" doesn't just mean "going faster"
Contrast with velocity: velocity tells you how position is changing; acceleration tells you how velocity is changing — one level removed

Quick example (conceptual, no calculation yet): A car goes from 0 mph to 30 mph in the first 5 seconds after a light turns green, then cruises at a steady 30 mph for the next 20 seconds. The car is accelerating during the first 5 seconds (velocity is changing) but NOT accelerating during the next 20 seconds (velocity is constant), even though it's still moving.

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.