A runner\'s arm swings rhythmically according to the equation y(t) = pi/5 cos[7p

Question

A runner's arm swings rhythmically according to the equation y(t) = pi/5 cos[7pi(t - 2/7]? where t?is time in seconds, and y(t)| is the angle between the actual position of the upper arm and the downward vertical position. Find the velocity of the angle: y'(t) =| Find the acceleration of the angle: y"(t) =| Find two times when the velocity is zero on the interval (0.214285714285714, 0.5)|. List your answers in order, smallest first. Smallest value where velocity is zero: Largest value where velocity is zero: Is y(t)? concave up or concave down at t = 5| seconds? Enter CU or CD: What does this concavity tell you about the runner's arm? The runner's arm is (speeding up/slowing down) at time t = 5|?

Explanation / Answer

velocity = y'(t)
v = (-7/5)*pi^2*(sin (7*pi*(t-2/7)))
I dont know why you have written it as
(-7/5)*pi^2*(sin (7*pi*(t))

v = (sin (7*pi*(t-2/7)))
it is 0 when
7*pi*(t-2/7) = 0 or 7*pi*(t-2/7) = pi
t = 2/7 ot t = 3/7

Answer: 1/7 s and 3/7 s

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