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Homework Help
Calculus and Beyond Homework Help
Particle's Equation, Velocity and Acceleration
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[QUOTE="defaultusername, post: 5487484, member: 595548"] [h2]Homework Statement [/h2] r([I]t[/I]) is the position of a particle in the [I]xy[/I]-plane at time [I]t[/I]. Find an equation in [I]x [/I]and [I]y [/I]whose graph is the path of the particle. Then find the particle’s velocity and acceleration vectors at the given value of [I]t[/I]. [ATTACH=full]101452[/ATTACH] [h2]Homework Equations[/h2] First derivative = velocity (velocity=distance/time) Second derivative = acceleration (acceleration=velocity/time) [h2]The Attempt at a Solution[/h2] To find the Equation, I first organize it into a set: [ e[sup]t[/sup], 2/9 e[sup]2t[/sup] ] Then I just plug in the value of t (ln3) [ e[sup]ln3[/sup], 2/9 e[sup]2(ln3)[/sup] ] I then reconstruct the original problem with the new values: r(t) = e[sup]ln3[/sup] i + 2/9 e[sup]2(ln3)[/sup] j r(ln3) = e[sup]1.0986[/sup] i + 2/9 e[sup]2.1972[/sup] j then I change the [I]i [/I]/ [I]j[/I] to [I]x/y[/I] r(ln3) = e[sup]1.0986[/sup] x + 2/9 e[sup]2.1972[/sup] y ----------------------------- As for velocity and acceleration, so far I have figured it like this: Velocity: [ e[sup]t[/sup], 2/9 e[sup]2t[/sup] ] [ te, 4/9 e[sup]t[/sup] ] Velocity = tei + 4/9e[sup]t[/sup]j Acceleration: [ e, 4/9 te] Acceleration = tei + 4/9 tej Am I taking the derivative correctly? As far as I know, e remains as e, even after the derivative, right? thanks in advance [/QUOTE]
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Particle's Equation, Velocity and Acceleration
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