AP Physics 1 · Exam guide
AP Physics 1 Translation Between Representations Explained: Diagrams, Equations and Graphs
The Translation Between Representations (TBR) question is worth 12 points, the most of any free-response question, with a suggested 25 to 30 minutes. You describe one scenario in several ways: a diagram, equations, and graphs, and then you justify why they agree or use them to predict a change. The numbers are made up for practice.
What the question asks
| Piece | What you do |
|---|---|
| Create a visual representation | Draw a diagram that describes the scenario, such as a motion diagram or a free-body diagram. |
| Derive equations | Write equations that are relevant to the scenario, in symbols. |
| Draw graphs | Sketch graphs that relate quantities in the scenario, with labeled axes. |
| Justify or predict | Explain why two of your answers agree or disagree, or use them to predict a change and justify it. |
A worked example
A cart starts from rest and accelerates at 2.0 m/s\(^2\). (a) Sketch a velocity-time graph. (b) Write equations for velocity and position. (c) Justify why the area under your graph agrees with your position equation at 3.0 s. (d) Predict the position at 3.0 s if the acceleration were doubled.
- The velocity-time graph is a straight line through the origin with slope 2.0 m/s\(^2\).
- \(v = 2.0t\) and \(x = \tfrac{1}{2}(2.0)t^2 = 1.0t^2\).
- At 3.0 s, the velocity is 6.0 m/s. The area under the graph is a triangle: \(\tfrac{1}{2}(3.0)(6.0) = 9.0\) m. The equation gives \(x = 1.0(3.0)^2 = 9.0\) m. They agree.
- With a doubled acceleration of 4.0 m/s\(^2\), \(x = \tfrac{1}{2}(4.0)(3.0)^2 = 18\) m.
It does not say what is being compared or why it must match.
It names the link between the two representations and uses the numbers to confirm it.
Habits for TBR questions
- Label every axis with the quantity and unit, and mark the points that matter.
- Keep your representations consistent with one another. A graph that disagrees with your equation costs points.
- In the last part, say which two things you are comparing and why they should agree.
- Do not skip the diagram. It often earns a point and guides the rest.
Common mistakes
- Drawing a graph with no labeled axes or units.
- Mixing up slope and area on a velocity-time graph.
- Writing an equation that does not match the graph you drew.
- A justification that says the results agree without saying why.
Frequently asked questions
How many points is Translation Between Representations worth?
12 points, with a suggested time of 25 to 30 minutes.
What counts as a representation?
A diagram, an equation, a graph, a table or a verbal description of the scenario.
Do I have to draw a good picture?
It should be clear and labeled, not artistic. Graders look for correct features, such as direction and labels.
What if my graph and equation disagree?
Check which is wrong, and explain the disagreement if you cannot fix it in time.
Where can I find the official scoring rules?
Exam formats change a little from year to year, so check the current course and exam description on the College Board site before test day.
Keep practicing
Every lesson in the AP Physics 1 course ends with practice items and an Exam focus box, and every unit has a ten-question practice set with worked answers. These free lessons also build the skills the free-response section tests:
See the AP Physics 1 course Free lessons and lesson list
More AP Physics 1 guides (4)
Start here
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