Where, How Fast, and Speeding Up or Not

You'll learnto read position, velocity and acceleration off one moving particle, and to tell speeding up from slowing down by comparing two signs.

A particle runs along a line, turns around, and comes back. Where is it, how fast is it going, and is it speeding up? Eleven short steps; press Next for each one.

11 STEPS · 6 QUICK CHECKS · AT REST IS v = 0, NOT s = 0 · SPEED IS |v| · SPEEDING UP COMPARES TWO SIGNS · v2

s(t) = t³ − 6t² + 9t − 2 ⇒ v(t) = 3t² − 12t + 9 ⇒ a(t) = 6t − 12

Before you start

What you're looking at

A particle on a number line, moving for four seconds. The arrow above it will be its velocity; the arrow below it, its acceleration.

The question

At any instant, is the particle speeding up or slowing down, and which function answers that?

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