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## Homework Statement

r(t)=ti+t^2j

Find the velocity, speed, acceleration, unit tangent, and unit normal vectors.

## Homework Equations

Velocity=r'(t)

Speed=magnitude of r'(t)

Acceleration=r''(t)

Unit tangent=r'(t)/magnitude of r'(t)

Unit normal=d/dt[unit tangent]/magnitude of d/dt[unit tangent]

## The Attempt at a Solution

Velocity=i+2tj

Speed=[itex]\sqrt{1^2+(2t)^2} = \sqrt{1+4t^2}[/itex]

Acceleration=2j

Unit tangent=[tex]\frac{i+2tj}{\sqrt{1+4t^2}}[/tex]

I'm pretty sure that's all right so far. I get mixed up in the algebra at the unit normal.

For d/dt[unit tangent] I have [tex]\frac{2j\sqrt{1+4t^2}-\frac{1}{2}(1+4t^2)^{-1/2}(8t)}{1+4t^2}[/tex].

Is that correct? How do I take the magnitude of that mess? I can't really see a way to simplify it.

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