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Topic 1.2: Practice Sheet — Instantaneous Velocity

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.

Warm-Up Level (straightforward, one-step)

  1. In your own words, explain the difference between average velocity and instantaneous velocity.
  2. A car's speedometer reads 42 mph at the exact moment you glance at it. Is this an average velocity or an instantaneous velocity? Explain how you know.

Standard Level (multi-step, matches typical AP Classroom depth)

  1. A ball's position is 4.90 m at t = 0.99 s and 5.10 m at t = 1.01 s (a very narrow time window around t = 1.00 s). Use this data to estimate the ball's instantaneous velocity at t = 1.00 s.
  2. A cart's position is 11.7 m at t = 2.9 s and 12.3 m at t = 3.1 s. Estimate the cart's instantaneous velocity at t = 3.0 s.
  3. A runner's average velocity for an entire 10-second sprint is 8 m/s. Explain why the runner's instantaneous velocity at t = 1 second (right after the start) was almost certainly NOT exactly 8 m/s.

AP-Level (multi-part: calculate + justify/represent/predict-a-change)

  1. A skater's position data near two different moments:

    • Near t = 2 s: position = 7.8 m at t = 1.95 s, position = 8.2 m at t = 2.05 s
    • Near t = 5 s: position = 14.9 m at t = 4.95 s, position = 15.1 m at t = 5.05 s

    a) Estimate the instantaneous velocity at t = 2 s and at t = 5 s. b) At which of these two moments was the skater moving faster? Justify using your calculated values, not just a guess. c) A classmate says using an even narrower time window (like 0.001 s on either side) would give a "more true" instantaneous velocity than the 0.05 s or 0.1 s windows used above. Are they right? Explain why or why not.

  2. If you only had access to a stopwatch that could measure time in whole seconds (no decimals), explain why you would NOT be able to directly measure a true instantaneous velocity, and describe what you'd be measuring instead.

Keep this sheet — it's part of your semester study materials, same as your Concept Sheets.