Mistake Master
Mistake Master · AP Physics C · Unit 7 · Topic 7.3 · Step-Through Animation
One Function and Its Derivatives
You'll learnhow velocity and acceleration follow from position as its first and second derivatives.
Simple harmonic motion is a single function — x(t) = A cos(ωt + φ) — and its calculus. Differentiate once for velocity, twice for acceleration; each derivative pulls down a factor of ω and slides the curve a quarter cycle. Stack all three on one clock and the whole choreography reads at a glance.
TRACE LAB
Before you start
What you're looking at
A block released from rest at full stretch, above three stacked graphs of position, velocity, and acceleration.
The question
When is the block moving fastest, and when is it accelerating hardest?
Watch for
At release the block is still (v = 0) while the spring pulls hardest — speed and force are out of step.
What the symbols mean
Three synced panels share one clock: position x, velocity v, acceleration a versus time; one cursor rides all three.
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