Reading Motion Graphs

Position-time and velocity-time graphs are packed with information, but you have to know where to look. On a position-time graph, the object's height on the graph tells you where it is, not how fast it's going. Speed lives in the slope: how quickly position changes per unit time. A steep line means position is changing fast, so velocity is large. A flat line, no matter how high up it sits, means velocity is zero. The same logic repeats one derivative up: on a velocity-time graph, the slope at any instant is the acceleration, because acceleration is the rate velocity changes.

For a straight-line graph, the slope is constant, so you can just compute rise over run between any two points. For a curved graph, the object's velocity or acceleration is changing, so you need the slope of the tangent line at the specific instant you care about, not the slope between two far-apart points. A curved velocity-time graph tells you acceleration itself is changing over time, something a straight line can never show, since a straight line only ever gives one constant acceleration value.

This graph-reading skill connects directly to the calculus underneath Unit 1: velocity is the derivative of position, acceleration is the derivative of velocity, and going backward, position is the integral of velocity. Reading slopes is the graphical version of taking a derivative, and later you'll read area under a velocity-time graph as displacement, the graphical version of integrating.