Posted by MEG on Monday, November 15, 2010 at 10:05pm.
max velocity occurs when the second derivative is zero
so ...
x(t) = 2πt + cos(2πt)
x '(t) = 2π - 2π(sin 2πt)
x ''(t) = 0 - 4π^2(cos 2πt)
= 0 for a max/min of velocity
cos 2πt = 0
2πt = π/2 or 2πt = 3π/2
t = 1/4 or t = 3/4
if t= 1/4
v(1/4) = x '(1/4) = 2π - 2π(sin π/2) = 2π - 2π = 0
if t=3/4
v(3/4) = 2π - 2π(sin 3π/2) = 2π + 2π = 4π
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