A Change Is Not a Position

You'll learnto read every integral in this topic as a change rather than a value, to add the starting position back, to tell displacement from total distance, and to decide whether a particle is speeding up from the signs of v and a together.

Integrating a velocity does not tell you where a particle is. It tells you how far it moved, and that number is signed, so a trip out and back can add up to almost nothing. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · AN INTEGRAL IS A CHANGE, AND A SIGNED ONE · v2

The area under a velocity is how far it moved, not where it is

Before you start

What you're looking at

The velocity of a particle moving along a line, and the region between that curve and the axis. Area above the axis is forward travel and area below it is backward.

The question

Is the question asking how much something changed, or what it now is, and does it want the net result or every meter actually covered?

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