5 Homework: Position to Velocity

  1. For each position graph, sketch the velocity graph. (This process is known as “taking the derivative”.)

  2. For each velocity graph, sketch the position graph. (This process is known as “integrating”.)

  3. The Consumer Price Index (CPI) is a number that correlates to how expensive it is to buy things. Suppose the CPI is increasing. Circle one of the bold choices for each problem.
    1. The CPI has positive or negative derivative.
    2. The CPI has positive or negative slope.
    3. Using the CPI as an indicator, consumer prices were higher or lower yesterday.
    4. Using the CPI as an indicator, consumer prices will be higher or lower tomorrow.
    Positive, positive, lower, higher

    ans
  4. The Beaverhead River Flow Rate (BRFR) measures how much water is flowing in the Beaverhead river. Suppose the BRFR has negative slope. Circle one of the bold choices for each problem.
    1. The BRFR has positive or negative derivative.
    2. The BRFR is increasing or decreasing.
    3. There will be more water or less water flowing in the river tomorrow.
    4. There was more water or less water flowing in the river yesterday.
    negative, decreasing, less water, more water

    ans
  5. The temperature of a chemical sample has a negative derivative. Circle one of the following bold options.

    Initially the sample was at room temperature. Then the sample was put in an oven or refrigerator.

    Refrigerator

    ans
  6. Acceleration is the measure of how quickly the velocity is changing. Suppose the velocity of a car is positive, but the acceleration is negative. Circle the bold option in each case.
    1. The position of the car is increasing or decreasing.
    2. The velocity of the car is increasing or decreasing.
    3. If the current trends continue, in five seconds the car will have a greater or smaller position number.
    4. If the current trends have held true for the last five seconds, five seconds ago the car was going faster or slower.
    Increasing, decreasing, greater, faster

    ans
  7. For each situation, try to sketch a picture of a graph matching the description.
    1. A graph with negative values (when I say values, I mean [latex]y[/latex]-values!).
    2. A graph with a positive derivative (when I say derivative, think slope!)
    3. A graph with negative derivative.
    4. A graph with positive derivative but negative values.
    5. A graph with negative acceleration.
    6. A graph with negative acceleration but positive derivative.

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Informal Calculus Copyright © by Tyler Seacrest is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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