- Draw the curve $r(t)=(t+2,t^2-4)$ for $0\leq t\leq 3$.
- Compute the velocity $\vec v(t)$ and speed $v(t)$ at any time $t$.
- At time $t=3$ state the position $\vec r(3)$ and velocity $\vec v(3)$, and then give a vector equation of the tangent line to the curve at $t=3$.
- Consider a different curve $\vec r(t) = (t^2, t^3)$. Find the arc length of this curve for $0\leq t\leq 2$.
- Consider the ray from the origin through the point $P=(-2,2)$. What's the angle between this ray and the positive $x$ axis? What the distance from the origin to $P$?
- Repeat the previous problem, but now with $P=(x,y)$.
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