Hi everyone, I am taking my first physics class (algebra based), and yesterday we were covering 1-Dimensional motion. I'm enrolled in Cal. 2, so I have some understanding of instantaneous velocity, etc. However, my professor said that instantaneous speed is always equal too instantaneous velocity, while average speed is only ever equal to the magnitude of the velocity vector, so long as there is no change in direction. The book we're going through did not explain this, so I'm having trouble understanding WHY, but let me test if my logic is correct. Average speed = magnitude of the velocity vector, so long as there is no change in direction, because if the direction changes, we subtract distance from it since we are only concerned about our displacement. However, with instantaneous velocity since our change in time is infinitesimally small, there is technically never any change in direction that time interval. So, essentially, the difference between instantaneous speed, and instantaneous velocity is solely that our velocity will be a vector (have direction) at that point, whereas instantaneous speed will only be a scalar. Is this right? And unrelated, are there any books that would be good for just explaining physics conceptually? I'm comfortable reading them if they are calculus based. My book I currently have just runs through example, after example, without really getting into the concepts. My professor, however, teaches mostly concepts. So I get a good mix. I'd just like something that can reiterate his points.