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 May 25th, 2012, 02:51 AM #1 Member   Joined: Jan 2012 Posts: 82 Thanks: 0 Velocity Hi Need some help on this A model car of mass m moves on a horizontal track so that its desplacement r from a fixed origin at the time t is given by r(t)=2cos(t)i+1/roots 2 sin(2t)j, Where 0 is equal to and great than t is equal or less than 2pi I need to determine the velocity and acceleration of the car at time t. Arron
 May 25th, 2012, 06:26 AM #2 Math Team   Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus Re: Velocity $r(t)=\left<2\cos(t),\frac{1}{\sqrt{2}}\sin(2t)\rig ht=>=$ $u(t)=r#39;(t)=\left<-2\sin(t),\frac{2}{\sqrt{2}}\cos(2t)\right>$ $a(t)=r'#39;(t)=\left<-2\cos(t),-\frac{4}{\sqrt{2}}\sin(2t)\right>$
 May 26th, 2012, 01:17 AM #3 Member   Joined: Jan 2012 Posts: 82 Thanks: 0 Re: Velocity Thank you so much. I just need to show that the car passes throught the origin exactly twice in the time interval and determine the two times. Can anyone help. Arron
May 26th, 2012, 03:25 AM   #4
Math Team

Joined: Nov 2010
From: Greece, Thessaloniki

Posts: 1,989
Thanks: 133

Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus
Re: Velocity

[color=#000000]In [0,2?] cos(t) and sin(2t) are zeroed simultaneously in ?/2 and 3?/2....here is the trajectory that looks like the infinity symbol.

[attachment=0:7blu6bwg]trajectory.gif[/attachment:7blu6bwg][/color]
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 trajectory.gif (4.4 KB, 287 views)

 May 26th, 2012, 06:51 AM #5 Member   Joined: Jan 2012 Posts: 82 Thanks: 0 Re: Velocity Thanks, Finally just need to determine the times at which the velocity of the car is perpendicular to its displacement and the position vector of the car at these times. Arron
 May 30th, 2012, 10:53 AM #6 Newbie   Joined: May 2012 Posts: 3 Thanks: 0 Re: Velocity Hi did you ever get anywhere with this?
 May 30th, 2012, 11:34 AM #7 Member   Joined: Jan 2012 Posts: 82 Thanks: 0 Re: Velocity I know I am not very good with this, but please could someone help me with the last point.
 May 31st, 2012, 04:23 AM #8 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 5 Re: Velocity Perhaps one of the reasons you are not very good at this is that you keep asking others to do it for you. You learn mathematics by doing mathematics, not by watching someone else do it.

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