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Have you taken calculus by any chance? And If so is this a calculus based class?

I can walk you through it but I need to think about how to tailor my approach based on your level.

Yes. This is calc based. I believe the derivative needs to be taken to solve this

Sorry I didnt see that you had returned hold on...

Ok is this the function you gave:

\[ r(t)= (c*t^{2} - (2d)*t^{3})i+((2c)*t^{2} - d* t^{3})j \]

Are you still there?

Internet failed

Hello

So if a particle is moving in the x-direction what does that mean?

I believe it is correct

I already tried t=c/3d and it said I was missing something

Specifically,
Your answer either contains an incorrect numerical multiplier or is missing one.

Does it mean in the POSITIVE x direction maybe?

Yes because it IS wrong.... The answer is all t NOT equal to that value

So I need to make an equation that excludes that point

Assuming any motion in the x-direction (either way) is permitted.

sure try 0

But that is just a guess

All of
0

So for all times 0 < t < c/(3d)

After that the velocity becomes negative (moves in the -x-direction) and stays that ways forever

Did you try that?

I don't know if I can put it in like that

I figured it out. Yay for physics roommate! Thank you for trying!!!

So what did the answer end up being?