Velocity and Acceleration as Derivatives · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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Velocity and acceleration as derivatives

Science · Forces & Motion · ages 18-19
Name ______________________   Date ____________

  1. With s(t) equal to 2t cubed plus 4t, what is v(t)?

    • 12t
    • 2t squared plus 4
    • 6t squared plus 4

  2. If s(t) is position, what are velocity and acceleration?

    • Velocity is the derivative of position, acceleration of velocity
    • Position is the derivative of velocity
    • Both equal the second derivative of time

  3. What does the sign of velocity tell you?

    • How fast the speedometer climbs
    • The direction along the axis
    • The value of acceleration

  4. For r(t) equal to the pair 3t squared and 5t, what is the acceleration vector?

    • The pair 6t and 5
    • The pair 6 and 0
    • The pair 6t and 0

  5. With s(t) equal to 2t cubed plus 4t, what is the acceleration at t equal to 3?

    Answer: ______________

  6. For r(t) equal to the pair t squared and 8t, what is the speed at t equal to 3?

    Answer: ______________

  7. Sam says the constant acceleration equations still apply when acceleration is 2t plus 3.

    Circle one:   True   False

  8. With a(t) equal to 5t, why do the constant acceleration equations stop applying?

    • Because acceleration changes with time
    • Because acceleration is always positive
    • Because motion needs two dimensions
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Velocity and acceleration as derivatives W1-mt_RdhbiJ6CTk-s1

  1. 6t squared plus 4 · Differentiate term by term: 2t cubed gives 6t squared and 4t gives 4.
  2. Velocity is the derivative of position, acceleration of velocity · Each step differentiates the last: position to velocity to acceleration.
  3. The direction along the axis · Positive points one way along the axis and negative the other.
  4. The pair 6 and 0 · Differentiate each component twice: 3t squared gives 6 and 5t gives 0.
  5. 36 · Differentiating twice gives a(t) equal to 12t, and 12 times 3 is 36.
  6. 10 · Velocity at 3 is the pair 6 and 8, whose length is 10.
  7. False · Sam is wrong: acceleration 2t plus 3 depends on time, so those formulas stay on the shelf.
  8. Because acceleration changes with time · Those equations assume fixed acceleration, so a changing 5t breaks them.
Worksheet · LightMySky