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## Homework Statement

The motion of a particle is defined as:

x=[(t-4)

^{3}/6]+t

^{2}

y=t

^{3}/6-(t-1)

^{2}/4

Find the acceleration and radius of curvature at t=2

## Homework Equations

a=(dv/dt)(e

_{t})+(v

^{2}/[tex]\rho[/tex])(e

_{n})

where e

_{t}and e

_{n}are the tangential and normal unit vecotrs to the curve and [tex]\rho[/tex] is the radius of curvature.

## The Attempt at a Solution

So I was able to get the acceleration by differentiating both of the equations twice and plugging in 2. The x component becomes 0 and the y is +1.5m/s. I'm stumped on the radius though. I differentiated to find dv/dt and v and tried solving for rho but it didn't work. That would have been essentially ignoring e

_{t}and e

_{n}since they are unit vectors, so the length is on it they shouldn't affect the outcome, right? Any ideas on how to solve the problem. Also, I think the way the equation is written with the unit vectors in there somewhat confuses me too so if there's anything that could help clear up any confusion with the equation that'd be great too.

Thanks!