Numerical problem

A particle is constrained to move in a circle with a 10-meter radius. At one instant,the particle’s speed is 10 meters per second and is increasing at a rate of 10 meters per second squared. Find the angle between the particle’s velocity and acceleration vectors.

Solution:
There are two perpendicular components of acceleration.
1) at along the direction of velocity,that increase the speed. so, at=10m/s2
2)ac centripetal acceleration,towards the center of rotation . ac=v2r=10m/s2
So, net a⃗ =a⃗ t+a⃗ c
|ac|=|at|, so it's equally inclined(at 450) to both components.