I'm stuck on how to do this problem:
$\displaystyle \vec{r}(t)=(\cos t)\,\vec{i}+(\sin t)\,\vec{j}, \qquad t \geq 0.$.
Does the particle have constant speed? (yes or no)
For this one I was thinking of finding the velocity and testing a lot of v values in the equation to see if it was constant.
Is the particle's acceleration vector always orthogonal to its velocity vector? (yes or no)
For this one I was thinking of finding the velocity and acceleration vector and using dot product to see if it was orgthagonal or not.
Does the particle move clockwise or counterclockwise around the circle? (clockwise, counterclockwise, both, or neither)
I am not sure for this one
Does the particle begin at the point (1,0)? (yes or no)
Not sure for this one.
i will appecriate the help! thank u!
Best Answer
The speed is defined as the norm of the velocity vector. Assuming the $r(t)$ is the placement, then you'll have to take derivative to get the velocity first. Still it's clear that the speed would be constant.
Again, we just need to compute the acceleration vector.
Just plug in $t=0$, $t=\frac{1}{2}$ and $t=1$ and see what you get.