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Say I have an acceleration vector in polar coordinates: a = -30e_r where the unit vector e_r points in the same direction as the Cartesian unit vector j.

How can I integrate that vector so that I have the velocity vector in polar coordinates?

I know that if I have an acceleration vector in Cartesian coordinates: a = -30j, I can integrate it with respect to time to get v = (-30t+v_0y)j + (v_0x)i.

I feel like integrating an acceleration vector in Cartesian coordinates is easier because i and j do not change as the tip of the vector moves around over time. However, with polar coordinates, e_r changes direction and yeah it gets messy.

Thanks.