Functions Involving Parameters, Vectors, and Matrices

If a rocket follows a flight path defined through the parameters $x(t) = 5t^2 - 2t + 3$ and $y(t) = t^3 - t^2 + 4$, how fast is it vertically traveling at the moment $t = 30$?

When the parametric equations $x(t) = \ln(t)$ and $y(t) = (\ln(t))^2$, their tangent section has curvature $K$ defined by $K = \frac{x''y' - y''x'}{(x'^2 + y'^2)^{3/2}}$, what is the value of $t$ where $K$ reaches its maximum?

If a ball’s height above ground over time can be described by parametric functions $h(t) = -16t^2 + v_0 t + h_0$ for its height $h$ in feet after being hit upward with initial velocity $v_0$ feet per second from initial height $h_0$ feet, what describes its vertical speed after rising for two seconds assuming no air resistance?

If you increase the parameter 't' uniformly on a smooth continuous path described by parametric equations, what happens to the location of points $(x(t), y(t))$ on its graph?

What describes the behavior of a particle moving along a path given by parametric equations if its speed increases without bound as time progresses?

What kind of discontinuity is present if the limits from both sides exist but are not equal?

Which set represents valid parametric equations for a linear function?

If a particle moves along a path given by the parametric equations $x(t) = e^t$ and $y(t)= e^{-t} + t^3$, what is its horizontal acceleration when $t=0$?

Which of the following represents a commutative property for addition?

What does The Elimination Method find when solving sets involving parameters like $S {X=T+5, Y=5-T }$?