Currently we're discussing uniform circular motion in my physics class. The previous unit discussed vectors and vector addition in the i, j, k format. When I try to apply the rules for vector addition to find the resultant velocity in uniform circular motion, I get an increase in the magnitude of the velocity vector. For example, say an object is in uniform circular motion around a circle of radius 2m with a tangential velocity of 6m/s. It's centripetal acceleration, v^2 / r, is therefore 18m/s^2 perpendicular to the direction of motion. So if the tangential velocity = 6i + 0j, and if the centripetal acceleration = 0i + 18j, the resultant vector would have a magnitude of sqrt(6^2 + 18^2) or about 19, which clearly isn't uniform circular motion. How should I think about this problem differently? Is it correct to add the initial velocity vector and the acceleration vector to find the final velocity, even though the units are different?