When a skater changes direction, so that the skater’s velocity changes as a vector quantity, is the skater accelerating?
Yes. Any change in a skater’s velocity involves an acceleration because acceleration is the change in velocity with time. So, if a skater is speeding up or slowing down, then it’s clear that the velocity changes because the speed part, the amount part a velocity, is changing. But when the skater’s velocity changes direction, so the skater is turning, even though the skater is traveling at the same speed, the skater is still undergoing acceleration and that acceleration still involves a net force on the skater, pushing the skater and bending the skater’s path.