- #1

## Homework Statement

So I am studying for my finals at the moment, and I came across a problem that I am not really sure how to assess. I am given that the velocity of a particle is determined by v

_{x}=12t

^{2}-5t, v

_{y}=15t

^{3}-6t. It wants me to find when the acceleration of the particle will be zero at time t. Because the equation is in parametric form, I am kind of confused by it, and am unsure of what I am supposed to use to determine the acceleration at a given time. The answer will also be never, but I am unsure how that is determined.

## Homework Equations

I thought maybe because acceleration is determined from the derivative of velocity, use (dy/dt)/(dx/dt) but after researching a little bit, I found the equation:

||a||=√((d

^{2}x/dt

^{2})

^{2}+(d

^{2}y/dt

^{2})

^{2})

## The Attempt at a Solution

So using the second equation:

||a||=√(24

^{2}+(90t)

^{2})

0=√(576+8100t

^{2})

0=576+8100t

^{2}

-576/8100=t

^{2}

√(-576/8100)=t

So this would seem like it is the correct way to assess the problem, considering t doesn't exist for a=0. Did I do this right? Or is there another way to do it? If so, what is the correct equation(s) to use?