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Cogito

AP Calculus BC · Chapter 1 · Lesson 3

Practice Worksheet

Vector-Valued Functions

Position, velocity and acceleration as vectors.

12 problems · about 22 minutes · CHA-3.G

NameDate

Figure — use these to answer the problems

Velocity is a vector with components. Its length is the speed, and its direction is the direction of travel.
  • Vector a(3, 4) · length 5
x component of velocity3
y component of velocity4
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. Velocity components 9 and 12. What is the speed?

    Answer

  2. What is the difference between distance travelled and displacement?

    • Distance integrates speed; displacement integrates velocity and can be zero.
    • They are two words for the same quantity.

  3. Velocity components 6 and 8. Speed?

    Answer

  4. Velocity components 5 and 12. Speed?

    Answer

  5. Position (t², t³) gives velocity (2t, 3t²). y component at t = 2?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Can speed be negative? 1 yes, 0 no.

    Answer

  2. Integrating speed gives what? 1 distance travelled, 2 displacement.

    Answer

  3. A particle returns to its start. What is its displacement magnitude?

    Answer

Stretch Yourself

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

4 problems

  1. Sort each quantity by whether it is a vector.

    Write each item under the heading it belongs to: Velocity · Acceleration · Speed · Distance travelled

    Vector

    Scalar

  2. Velocity components 8 and 15. Speed?

    Answer

  3. The Speed

    Velocity components 3 and 4. What is the speed?

    Answer

  4. The Velocity

    Position (t², t³) gives velocity (2t, 3t²). What is the x component at t = 3?

    Answer