Final answer:
The angle between the particle's velocity and acceleration vectors in circular motion is 180 degrees.
Step-by-step explanation:
The angle between the velocity and acceleration vectors can be calculated using trigonometry.
The velocity vector represents the direction and magnitude of the particle's motion. In circular motion, the velocity vector is tangent to the circle at any point. The acceleration vector represents the rate at which the velocity is changing. For circular motion, the acceleration is directed towards the center of the circle.
When a particle is moving in a circle and speeding up, its acceleration has two components: tangential acceleration that is responsible for changing the speed, and centripetal acceleration that is always directed towards the center of the circle.
The velocity of the particle is always tangent to the circle. In this case, since the given rate of increase of speed (tangential acceleration) and the speed itself are equal (both 10 m/s and 10 m/s² respectively), the two acceleration vectors form an isosceles right triangle with the velocity vector.
Therefore, the angle between the velocity and the total acceleration vector is 45 degrees.