This is a two-dimensional kinematics question:
A particle's position coordinates (x,y) are (2m, 3m) at t=0; (6m, 7m) at t=2s, and (13m, 14m) at t=5s. Find the average velocity vector between t=0s and a) t=2s, b) t=5s.
I don't know how to find this without acceleration being given.
You don't need to know the acceleration.
For average velocity, just divide the position change vector by the time interval.
Between t= 0 and 2s, the x position increases by 4 m and the y position increases by 4 m.
The average velocity components are
Vx = 2 and Vy = 2.
Do the 5 second case the same way.