Representing Motion
A motion graph plots one of three numbers: position, velocity, or acceleration. The line on the page tracks that one number changing over time. It is not a picture of where the object went. Two moves get you almost everything: read a slope (how fast the y-axis number is changing) or read an area (how much it added up to over the interval).
The quantity on the y-axis decides what those two moves give you. On a v-t graph, slope is acceleration and area is displacement. On an x-t graph, slope is velocity. The most expensive mistakes on this topic come from picking the wrong move (slope when the question wants area), or treating the line on the page as a picture of the path. Neither is what the line is for.
The work
3 ways in · any order
Lesson
Representing Motion
›
A motion graph is not a picture of the path. The lesson teaches how to read x-t, v-t, and a-t graphs as the slope-and-area machines they actually are, then closes with a ten-scenario applet that drills graph-as-picture, slope-vs-area, and the velocity-vs-acceleration confusion that catches motion graphs in particular.
Diagnostic
10-item topic check
›
Ten items on the graph-reading misconceptions: reading a position-time graph as a literal picture of the path, confusing slope of one curve with area under another, and treating velocity and acceleration as interchangeable when both are encoded in the same graph.
Targeted Practice
Drill a single misconception
›
Pick one of the failure modes you've missed and grind it on its own. The round is adaptive: two correct in a row clears the misconception and you move on.