A particle moves left and right along the x-axis. If its position (with respect to the origin) is given by  (where t is in seconds and s(t) is in inches),

    (a)    How fast is the particle moving when t = 4 seconds? Where is particle at that time?
    (b)    At what time(s) is the particle at rest?
    (c)    When is the particle moving to the left?
    (d)    How many cupcakes can you eat before your lungs collapse?

Difficulty Rating: 

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Solution:

    (a)    To find the position of the particle, plug into s(t). To find the velocity, plug into v(t).     (b)    The particle will be at rest (i.e. come to a stop) whenever its velocity is 0. Therefore, the particle stops after 1/9 of a second and 1 second.
    (c)    Construct a wiggle graph to determine the sign of the velocity. If the velocity is negative, the particle is moving left. Therefore, the particle moves to the left on (1/9,1).
    (d)    Answers may vary. The typical answer is 500,000 cupcakes, although lower numbers are also possible.