Parametric Equations, Polar Coordinates, and Vector–Valued Functions (BC Only)

A particle travels along a path described by parametric equations $x=t\cos(t)$ and $y=t\sin(t)$; what describes its motion between times $T_1=0$ and $T_2>0$?

If a point moves along a path described by parametric equations $x(t)=e^{2t}$ and $y(t)=e^{-t}$, how does its speed change as time increases?

How would you express the point at a distance of 5 units from the pole at an angle of $\pi/2$ radians in polar coordinates?

Given a position function in the form $\mathbf{s}(t) = \langle t^3 - t, t^2 + t \rangle$, for what value of $t$ is there no horizontal movement?

What is the polar coordinate equivalent of the origin in Cartesian coordinates?

A particle moves along a curve in the plane with a velocity vector given by $v(t) = \langle 2t, 4t^3 \rangle$. If the particle’s initial position is $\langle 1, 4 \rangle$, what is the position vector of the particle at time $t = 2$?

Which of these points lies on the terminal side of an angle that measures $\pi$ radians in polar coordinates?

What does it mean if the ratio test for a series $\sum a_n$ yields $\lim_{n \to \infty} \left| \frac{a_{n+1}}{a_n} \right| = L$ where $0 < L < 1$?

A particle's motion in space is described by vectors; what component determines its vertical change?

A projectile following parametric equations $x(T) = T^2 , Y(T) = -16(T)^2 + 100T$ How long will it take before reaching maximum height?