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AP Physics 1 · Unit 1 · Kinematics

Graphing Acceleration Practice Problems

Connect position, velocity, and acceleration graphs for the same trip. Interpret turning points, areas, delayed starts, and catch-up motion through six conceptual and six calculation questions.

12 questions6 conceptual · 6 calculation

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Simulation scene from the Graphing Acceleration lesson.Open interactive practice
A scene from the related lesson. Open the practice to work through the questions.

What you’ll practice

Move between three views of one trip

Translate between graphs

Use velocity–time slopes to identify acceleration and position–time slopes to identify velocity. Explain what happens when a graph crosses zero.

Use area over an interval

Find displacement from velocity–time area and velocity changes from acceleration–time area. Separate positive and negative regions.

Analyze trips with several stages

Combine acceleration, cruising, braking, and waiting. Compare two carts using a shared time origin to decide when they meet.

A question from this set

A falling line and a change of direction

Which description matches this velocity–time graph over the entire interval?

  • The cart slows down throughout because the line slopes downward.
  • The cart moves right while slowing, reverses at zero velocity, then moves left while speeding up.
  • The cart stays on the right side of the origin throughout because the slope never changes.
Try it in the practice set
Given velocity–time graphHorizontal axis: time in seconds. Vertical axis: v in m/s. Survey cart: at 0 seconds, 6 m/s; at 3 seconds, 0 m/s; at 4 seconds, -2 m/s-4-20246801234v (m/s)t (s)
The given velocity–time line crosses zero during the interval.

Key ideas

Read each axis before interpreting the shape

A zero velocity can mark a turnaround

At a turning point, velocity passes through zero while acceleration may stay nonzero. A position curve then changes from increasing to decreasing, or the reverse.

Area preserves direction

Regions above and below zero contribute with opposite signs to displacement on a velocity graph. Total distance instead adds the magnitudes of the traveled segments.

See the physics

Match the graph to the recorded trip

After checking your response, run the cart and compare its position, velocity, and acceleration views. Delayed-start and chase questions use parallel lanes so the two motions can be compared on one clock.

Use a hint for a starting point or open a worked solution to follow the reasoning. Your progress saves in this browser, so you can return to unfinished questions.

Ready for graphing acceleration?

Begin with a conceptual question, then work through the calculations.

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