Finding Particle's Velocity and Acceleration Vecotrs

[Alex23]

[h=2]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.

r(t)=(e^t)i + ((2/9)e^(2t))j at t= ln 3

I know I have to first solve for t using

x=e^t and
y=(2/9) e^(2t)

but I don't know how to solve for t from here. I just need like the first 2 steps then I can do the rest by myself.

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[burakaltr]

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.

r(t)=(e^t)i + ((2/9)e^(2t))j at t= ln 3

I know I have to first solve for t using

x=e^t and
y=(2/9) e^(2t)

but I don't know how to solve for t from here. I just need like the first 2 steps then I can do the rest by myself.

Start out
e*t=x

what is y ?

What do you get for the first and second derivatives wrt t ?

 

[Alex23]

I thought y was y=(2/9) e^(2t)

 

[burakaltr]

I thought y was y=(2/9) e^(2t)

In what way are they related to each other ?

Can you find y(x)= y in terms of x where x is always e**t

 

[Alex23]

Are they related like x^2 + y^2 = 1

or


If i can solve for t, then I can plug that value into y equation.

 

[Deleted member 4993]

Are they related like x^2 + y^2 = 1

or


If i can solve for t, then I can plug that value into y equation.

What part of the problem - makes you think that you need to solve for "t"?

 

[Alex23]

What part of the problem - makes you think that you need to solve for "t"?

I did another question similar this one and I had to solve for t in that question.

In that question r(t)=(t+1)i + (t^(2)-1)j , t=1

I did :

x=t+1
y=t^(2)-1

t=x-1 and t^2=x^2-2x+1

Then I plugged that t^2 value into y equation and got y=x^2-2x

 

[Alex23]

Never mind I got the answer.