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November 22, 2014

November 22, 2014

Posted by **MEG** on Monday, November 15, 2010 at 10:05pm.

- Calculus -
**Reiny**, Monday, November 15, 2010 at 10:22pmmax 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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