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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: /0 on July 15, 2009, 09:51:13 pm

Title: Kinematics
Post by: /0 on July 15, 2009, 09:51:13 pm: $v=\cos{\frac{1}{2}t }$ , $t \in [0, 4\pi]$ $(x_o,t_o) = (\frac{1}{2}, 0)$

Find dsplacement in terms of velocity?

Answer: $x=2\sqrt{1-v^2}+0.5$

How can this be if the displacement is negative at times?

NVM SOLVED
Title: Re: Kinematics
Post by: dcc on July 16, 2009, 02:13:34 pm: Displacement can be negative.
Title: Re: Kinematics
Post by: /0 on July 16, 2009, 07:30:06 pm: Yes, I realised the solution was a hybrid function:

$x = \begin{cases} 2\sqrt{1-v^2}+0.5 & 0 \leq t \leq 2\pi \\ -2\sqrt{1-v^2}+0.5 & 2\pi < t \leq 4\pi \end{cases}$