Motion graphs, step by step
What you will learn: how a motion (standing, steady, speeding up, slowing down, ramps and hills) shows up on the position, velocity and acceleration graphs.
Make your prediction in the "Your prediction" box (below the graphs on a phone), then press Reveal to play.
Slope of the position graph = velocity. Slope of the velocity graph = acceleration. A dotted line on the a-t graph marks a jump (where the slope of the track changes). x and v never jump.
Your prediction. Pick one shape for each graph, then press Reveal.
Play around (change this step's motion)
Keys: ← → change step, space = play/pause, r = replay.
Step 12: Review: every shape in one table
Each row is a step you watched (lesson values). Top graph follows your Position / Distance choice: position. Press a row's button to go back to it.
| Motion | x-t / d-t | v-t | a-t |
|---|
Rules of thumb: flat v-t means a = 0. v and a in the same direction means speeding up; opposite directions means slowing down. On a straight slope a = g sin θ, constant, so v-t is a straight line. A bend in the track makes a jump, never v.
Try this
- At the turning point in step 6 the cart's velocity is zero. Is its acceleration zero there too?
No. v = 0 for an instant, but v is still changing (from + to −) at −1 m/s². Acceleration is how fast v changes, so it stays −1 m/s² the whole time. - On a v-t graph, how can you tell an object is slowing down, even when v is negative?
The line is heading toward the time axis (v getting closer to 0). Speed is the size of v. In step 11, on the left slope v goes from −6.9 m/s toward 0: slowing down, with a positive. - In step 11, why does position go down while distance goes up?
Position is measured from the left end and the cart moves left, so x gets smaller. Distance is the total path length covered, which can only grow (or stay the same when the object is still).