Question Type 6: Determining speed and velocity for trajectories with varying velocities Exercises

For the same trajectory r(t) = (1,0) + tigl(8 + t,\,2 - t^2igr), find $v(t)$ and the speed at $t = 2$.

For the trajectory defined by r(t) = (1,0) + tigl(8 + t,\,2 - t^2igr), find the velocity vector $v(t)$ and compute the speed at $t = 1$.

For r(t) = (1,0) + tigl(8 + t,\,2 - t^2igr), find all times when the motion is purely horizontal. (Motion is purely horizontal when $y'(t)=0$.)

For r(t) = (1,0) + tigl(8 + t,\,2 - t^2igr), find all times when the motion is purely vertical. (Motion is purely vertical when $x'(t)=0$.)

For r(t) = (3,4) + tigl(9 - t^2,\,11 + tigr), find all times when the motion is purely vertical. (Solve $x'(t)=0$.)

For r(t) = (3,4) + tigl(9 - t^2,\,11 + tigr), find the time when the motion is purely horizontal. (Solve $y'(t)=0$.)

For r(t) = (1,0) + tigl(8 + t,\,2 - t^2igr), determine whether there is any real time when the velocity components are equal, i.e. $2-3t^2 = 8+2t\,.$

For $r(t) = (3,4) + t\bigl(9 - t^2,\,11 + t\bigr)$, find the speed at the time when the motion is purely horizontal.