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Grade 12 · Math · Calculus

12th grade Position, velocity, speed and acceleration worksheet

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Position, velocity, speed and acceleration

Grade 12 Math Worksheet - Building Confidence

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  1. A toy cart is at s(t) = 2t³ − 9t² + 12t meters after t seconds. Ari finds its velocity at t = 4. What is it, in m/s?

  2. A robot is at s(t) = 3t³ − 6t² + 2t meters after t seconds. Bo finds its velocity at t = 2. What is it, in m/s?

  3. A toy train is at s(t) = 2t³ + 3t² − 12t meters after t seconds. Esme finds its velocity at t = 1. What is it, in m/s?

  4. A sled on a track is at s(t) = 4t³ − 3t² − 6t meters after t seconds. Jun finds its velocity at t = 2. What is it, in m/s?

  5. A toy train has velocity v(t) = −2t² + 8t + 1 m/s. Luz finds its acceleration at t = 1. What is it, in m/s²?

  6. A sled on a track has velocity v(t) = 4t² − 7t + 3 m/s. Milo finds its acceleration at t = 2. What is it, in m/s²?

  7. A toy cart has velocity v(t) = 5t² + 2t − 6 m/s. Noah finds its acceleration at t = 3. What is it, in m/s²?

  8. A toy train has velocity v(t) = t² − 6t + 5 m/s, with right as positive. Pia checks t = 2. Which describes the motion?

    • moving left, speed 2 m/s
    • moving left, speed 3 m/s
    • moving left, speed −3 m/s
    • moving right, speed 3 m/s

  9. A sled on a track has velocity v(t) = t² − 4t − 1 m/s, with right as positive. Ren checks t = 5. Which describes the motion?

    • moving left, speed 4 m/s
    • moving right, speed 6 m/s
    • moving right, speed 4 m/s
    • moving right, speed −4 m/s

  10. A toy cart has velocity v(t) = −2t + 8 m/s, with right as positive. Tala checks t = 6. Which describes the motion?

    • moving left, speed 4 m/s
    • moving right, speed 4 m/s
    • moving left, speed −4 m/s
    • moving left, speed 2 m/s
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12th grade Position, velocity, speed and acceleration worksheet – printable
Print: 123456

About this worksheet

Position, velocity, speed and acceleration. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can find velocity and acceleration from a position formula.
  • I can tell the direction, the speed, and whether an object speeds up.
  • I can find when an object is at rest and how far it travels.

Standard: none (beyond CCSS)

Words to know

velocity v(t): s′(t): how fast and which way position changes.

acceleration a(t): v′(t): how fast velocity changes.

Common mistakes

Gave the position instead of the velocity. Velocity is s′(t).

Gave the acceleration (the second derivative) where the question asked about velocity or speed.

Gave the velocity where the question asked for acceleration or speed.

Questions parents ask

What is the most common mistake with position, velocity, speed and acceleration?

Gave the position instead of the velocity. Velocity is s′(t).

Are these 12th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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