# Calculus

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The height (in feet) at time t (in seconds) of a small weight oscillating at the end of a spring is given below.
h(t) = 0.2 cos(2t)

(a) Calculate the weight's average velocity over the time intervals [1, 2] and [5, 7].

• Calculus -

v = dh/dt = -0.4 sin(2t)

average v from t = 1 to t = 2 is
(Integral of v dt from 1 to 2)/(2-1)
= [h(2)-h(1)]/(2 -1) = [-.1307 -(-0.0832)] = -0.0475 ft/s

You can do the other interval yourself

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