Geeze you have the word physics in your name....
Interesting way they have you do it, looks like they're purposefully trying to make you do more work than you need to. But then again finding the average acceleration is a bit more work for circular motion than instantaneous acceleration
First set up your coordinate system, polar coordinates would be a breeze but I'm guessing this problem wants Cartesian, so draw a circle, a find a place for your origin i.e. (0,0), my suggestion, right through the center of the circle, this way you exploit the symmetry of the circle.
Finding the first vector really is arbitrary, its a uniform speed in a circle, so any point you choose as
V1 is going to be fine, lets make it easy, choose one that's right along either the x or y axis.. that way it will only have velocity components in the y or x direction (respectively), and the magnitude will be the velocity value that's given 5.60 m/s
The second vector,
V2, requires a bit of work, and it depends upon your delta-t. Figure out how far the dog will go in that delta-t (using the velocity given) and that will be how much of that circle the dog will have gone. v * delta t = distance. Then you can work backwards and find what angle that is given remembering (hopefully) that the arclength of a circle (i.e. the distance traveled by the dog) [ s = r * angle ], a little bit of manipulation can get you that angle, and from there some sines and cosines should hopefully yield your x & y components of
V2 and from there it should be a snap.
Let me know if this didn't help