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March 25, 2017

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If a ball is thrown in the air with a velocity 44 ft/s, its height in feet t seconds later is given by y = 44t - 16t2.

(a) Find the average velocity for the time period beginning when t = 2 and lasting 0.5 second.
ft/s

(b) Find the average velocity for the time period beginning when t = 2 and lasting 0.1 second.
ft/s

(c) Find the average velocity for the time period beginning when t = 2 and lasting 0.05 second.
ft/s

(d) Find the average velocity for the time period beginning when t = 2 and lasting 0.01 second.
? ft/s

(e) Estimate the instantaneous velocity when t = 2.

  • Calculus - ,

    This will not use calculus. It is an exercise to show how to use algebra to approximate the instantaneous velocity that you would get using calculus.
    Just use the formula
    y = 44t - 16 t^2
    multiple times.
    For (a), y(2) = 88 - 64 = 24 ft
    y(2.5) = 110 - 100 = 10 ft
    Average velocity Vav
    = [y(2.5) - y(2)]/0.5 = -28 ft/s
    For (d), y(2.01)= 88.440 - 64.6416 = 23.7984
    Vav = [y(2.01) - y(2)]/0.01
    = (23.7984 -24)/0.01 = -20.16 ft/s

    Do parts (b) and (c) yourself and notice the trends in average velocity as the time interval gets shorter

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