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As a cheetah runs, its velocity is given by   where is measured in feet per second.

  1. Sketch a graph of the cheetah’s velocity.

    Piecewise increasing curve, left red curve labeled Piece 1, starts at the origin opening up, ending at (2, comma 48), right blue curve labeled Piece 2, starting at (2, comma 48), ending at (4, comma 192).

  2. Approximately how fast is the cheetah running at second? How did you get your answer?

    This is a velocity function. So, what is the value at ?

  3. To catch prey, such as an antelope, the cheetah runs for seconds. Approximately how far does the cheetah need to run to catch its prey? Describe your method.

    Use geometry to approximate the area under the curve.

    Trapezoid Method ft
    Midpoint Method ft
    There are other valid geometric methods.

  4. Annalou the Antelope standing feet north of the Great Pond. The cheetah spots Annalou and runs south in a direct line towards her, catching her in exactly seconds. What was the cheetah’s initial position relative to the pond?

    Your answer in part (c) is an approximation of how far the cheetah traveled in seconds. At , Annalou was only feet north of the pond. Where was the cheetah?