- #1

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## Homework Statement

r(

*t*) is the position of a particle in the

*xy*-plane at time

*t*. Find an equation in

*x*and

*y*whose graph is the path of the particle. Then find the particle’s velocity and acceleration vectors at the given value of

*t*.

## Homework Equations

First derivative = velocity

(velocity=distance/time)

Second derivative = acceleration

(acceleration=velocity/time)

## The Attempt at a Solution

To find the Equation, I first organize it into a set:

[ e

^{t}, 2/9 e

^{2t}]

Then I just plug in the value of t (ln3)

[ e

^{ln3}, 2/9 e

^{2(ln3)}]

I then reconstruct the original problem with the new values:

r(t) = e

^{ln3}i + 2/9 e

^{2(ln3)}j

r(ln3) = e

^{1.0986}i + 2/9 e

^{2.1972}j

then I change the

*i*/

*j*to

*x/y*

r(ln3) = e

^{1.0986}x + 2/9 e

^{2.1972}y

-----------------------------

As for velocity and acceleration, so far I have figured it like this:

Velocity:

[ e

^{t}, 2/9 e

^{2t}]

[ te, 4/9 e

^{t}]

Velocity = tei + 4/9e

^{t}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