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Cogito

AP Calculus AB · Chapter 4 · Lesson 1

Practice Worksheet

Motion and Related Rates

Derivatives with units attached.

11 problems · about 25 minutes · AP Calculus AB 4.1, 4.4, 4.5

NameDate

Figure — use these to answer the problems

Read the position curve as a journey. The tangent slope is the velocity.
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y = 1x³ − 4x + 0
  • Point(1, -3)
  • Slope of the tangent-1
a1
b-4
c0
Time1
Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. Velocity −4, acceleration 6. Speeding up? 1 for yes, 0 for no.

    Answer

  2. Velocity 5, acceleration 2. Speeding up? 1 for yes, 0 for no.

    Answer

  3. Velocity 5, acceleration −2. Speeding up? 1 for yes, 0 for no.

    Answer

  4. Velocity −6, acceleration −3. Speeding up? 1 for yes, 0 for no.

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Order the steps of a related-rates problem.

    Write 1 to 4 in the boxes to put these in order.

    • Write a relationship between the quantities
    • Differentiate both sides with respect to time
    • Substitute the known values and rates
    • Solve for the unknown rate

  2. Position s(t) = t². What is the velocity at t = 3?

    Answer

  3. Same position function. What is the acceleration?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Velocity −3. Is the object moving forwards? 1 for yes, 0 for no.

    Answer

  2. Speed is 9 and the object moves backwards. What is the velocity?

    Answer

  3. Speed

    Velocity is −7. What is the speed?

    Answer

  4. At Rest

    An object is momentarily at rest. What is its velocity?

    Answer