Topic 1.3: Practice Sheet — Position-Time Graphs
Name: _______________________________ Date: _______________ Period: ______
Directions: Show your work for every problem — a correct answer with no work shown earns partial credit at best. Circle or box your final answer. Several problems ask you to sketch a graph — use the grid space provided or your own graph paper, and always label your axes with units.
Warm-Up Level (straightforward, one-step)
- A skateboarder's position is 0 m at t = 0 s and 12 m at t = 4 s, moving in a straight line the whole time. Find the slope of the position-time graph (which equals the velocity).
- Sketch a position-time graph for an object that starts at position 0 and moves at a constant velocity of 3 m/s for 5 seconds.
Standard Level (multi-step, matches typical AP Classroom depth)
- Use this position-time data table for a cart:
| Time (s) | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Position (m) | 0 | 2 | 4 | 6 | 8 |
Find the velocity (slope) between t = 0 s and t = 4 s.
- A different cart's data table:
| Time (s) | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Position (m) | 0 | 3 | 6 | 6 | 6 |
Find the velocity during the interval from t = 0 to t = 2 s, and the velocity during the interval from t = 2 to t = 4 s. Describe in words what the object was doing during each interval.
- Sketch a position-time graph for this story: "A person stands still for 2 seconds, then walks backward (toward negative position) at a steady pace for 3 seconds."
AP-Level (multi-part: calculate + justify/represent/predict-a-change)
- Use this position-time data table:
| Time (s) | 0 | 2 | 4 | 6 |
|---|---|---|---|---|
| Position (m) | 0 | 10 | 10 | 4 |
a) Find the velocity for each of the three intervals (0-2 s, 2-4 s, 4-6 s). b) Which interval represents the object moving fastest, and how do you know from the numbers (not just "it looks steeper")? c) Describe, in words, what this object physically did over the full 6 seconds.
- An object's position-time graph is a straight line with a slope of 4 m/s over a 10-second interval. If the same object had covered the exact same total displacement in only 5 seconds instead, would the slope of its new graph be steeper, less steep, or the same? Explain your reasoning first, then calculate the new slope to check.
Keep this sheet — it's part of your semester study materials, same as your Concept Sheets.