so I have a question on solving the following:
"A particle moves around the circle $x^2+y^2=25$ at constant speed, making one revolution in 2s. Find its acceleration?"
In the solution it says, that it's easy to see that the position vector is given by $$\textbf{r}=5cos(\omega t)\textbf{i}+5sin(\omega t)\textbf{j}$$ but unfortunately for me is not so easy to see, why can I say that this is the vector position? Does the formula $\textbf{r}=acos(\omega t)\textbf{i}+bsin(\omega t)\textbf{j}$ only hold for circles (does this formula has a name?)?
and the last thing I want to ask is with one revolution, do they mean that the particle has travelled one cicle?
If you know the answer and would like to share it, it would be very much appreciated
Thanks in advance!
Hint: what is the paramtric form of a point on the circle?
This corresponds to the position of the rider at any time t.
For your second question, yes, this means the particle has travelled one full circle, from starting point to starting point.