13-4 Motion in 3-D

13-4 Motion in 3-D - 2 /16 0 = 2-y 2 /16 y 2 /16 = 2 y 2 =...

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13.4 Motion in 3-D - Path of the moving object r -> (t) = <2-t,4(t) 1/2 > <= The equation of the path Suppose @ P(t=1) **t is time - Velocity of the object? - Acceleration of the object? - Speed? r -> (t) = r -> ' (t) = <-1, 2t -1/2 > = <-1, 2/(t) 1/2 > | t=1 = <-1,2> (1) t = 20x (2) y 2 = 16t -sub (2) into (1) y 2 / 16 = 2-x x = 2 - y
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Unformatted text preview: 2 /16 0 = 2-y 2 /16 y 2 /16 = 2 y 2 = 32 y = (32) 1/2 Q: is V-&amp;gt; perp. to a-&amp;gt; ? A: NO Q 2 : When is V-&amp;gt; perp. to a-&amp;gt; true? A: When ||V-&amp;gt; || is constant. a-&amp;gt; (t) = v-&amp;gt; ' (t) = &amp;lt;0,-t-3/2 &amp;gt; = &amp;lt;0,-1/t 3/2 &amp;gt; | t=1 = &amp;lt;0,-1&amp;gt; v-&amp;gt; (dot) a-&amp;gt; = 0 &amp;lt;0,-1&amp;gt; (dot) &amp;lt;-1,2&amp;gt; = 0-2 != -2...
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This note was uploaded on 03/13/2008 for the course MATH 214 taught by Professor Riggs during the Spring '05 term at Cal Poly Pomona.

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13-4 Motion in 3-D - 2 /16 0 = 2-y 2 /16 y 2 /16 = 2 y 2 =...

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