Motion Graph Analysis

Choosing What to Practice

• Use the GRAPH buttons to pick x–t, v–t, a–t, or Mixed. Mixed gives you a random graph type each time, which is the best choice for review before a quiz or test.

• Use the LEVEL buttons to set the difficulty. Easy graphs are a single straight segment, and Hard graphs have several segments and ask about specific time intervals.

• Use SKILL PRACTICE to drill one skill at a time, or leave it on All skills. On x–t graphs you can focus on Displacement, Distance, Instant velocity, or Average velocity. On v–t graphs you can focus on Displacement, Change in velocity, Instant acceleration, or Average acceleration. The a–t graph only asks for change in velocity, so it has no skill buttons.

• Note for teachers: Each skill button is a good fit for targeted remediation. If a student keeps mixing up displacement and distance, have them stay on those two x–t skills until they stop missing them.

Answering a Question

• Read the graph first, then check the question to see which time interval it asks about. Type your answer in the box, with the units shown beside it, and press Check.

• The "0 / 0 correct" counter in the top corner tracks how many you have gotten right out of the questions you have attempted.

• Press New Problem any time to get a fresh graph. Graphs are randomly generated, so you will never run out of practice.

• Mastery tip: Before you type anything, say out loud what the question is asking for (a slope, an area, or a final minus initial value). Most missed questions come from using the wrong method, not from arithmetic errors.

Hint and Worked Solution

• If your answer is wrong, the tool says "Not quite" and draws a hint directly on the graph, such as the shaded area you need. Use it to try again before looking at the solution.

• Press Hint at any time to see the hint without checking an answer, and press Hide hint to remove it.

• Press Show worked solution when you are stuck. It walks through the method on the graph itself. Compare it with your own work to find where your approach went wrong.

• Mastery tip: Try again after a hint before opening the worked solution. Finding the mistake yourself builds the skill far better than reading the answer.

Reading the Graph (Reference Panel)

• The reference panel next to the question lists the relationships for the graph you are on. It changes with the graph type.

• On x–t graphs, slope is velocity, final minus initial is displacement, the sum of the size of each segment's change in position is distance, and the slope of the line from start to end is average velocity.

• On v–t graphs, slope is acceleration, area under the graph is displacement, final minus initial is change in velocity, and the slope of the line from start to end is average acceleration.

• On a–t graphs, area under the graph is change in velocity.

• Note for teachers: The panel is there to support students as they build the habit. Once a student is consistently correct, have them cover it and answer without it.

Sign Convention

• Negative velocity means the object moves in the negative direction.

• Area below the time axis counts as negative. On a v–t graph that means negative displacement, and on an a–t graph it means a negative change in velocity.

• Distance is never negative, because it adds up how far the object traveled regardless of direction. Displacement can be negative.

• Mastery tip: On an x–t graph where the object turns around, find displacement and distance back to back. Seeing two different answers from the same graph is the fastest way to lock in the difference.