Topic 1.2: Instantaneous Velocity

Name: _______________________________ Date: _______________

Before We Start: Yesterday's Recap

Last class we learned about position-time graphs. Without looking back: what does the slope of a position-time graph tell you?

Today's New Concepts

AP CED Alignment: Unit 1, Topic 1.B

Average Velocity (reminder)

Velocity calculated over an entire time interval — the "whole trip" number
Formula: $v_{avg} = \dfrac{\Delta x}{\Delta t}$

Instantaneous Velocity

An object's velocity at one specific moment in time — not averaged over anything
Think of it as what a speedometer shows you right now, at this exact second
On a position-time graph, instantaneous velocity at a point equals the slope of the tangent line at that exact point (the steepness right at that spot — no calculus needed, just visualize it)
On a straight-line section of a graph, instantaneous velocity and average velocity are the same number
On a curved section, they're usually different — that's exactly when this distinction matters

Worked Example: A cheetah can hit an instantaneous speed of 60-70 mph during a short sprint — that's the "right now" number. But over an entire 20-second hunt (sprint, then slow down, then stop), its average velocity for the whole chase is much lower, because it can't sustain that peak speed the whole time.

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.