1. The problem statement, all variables and given/known data I have somewhat general question about time derivative of a vector. If we have r=at2+b3it's easy to find instantaneous acceleration and velocity(derivative with respect to dt) v=2at+3bt2 a=2a+6btBut consider this position vector r=b(at-t2)where b is constant vector and a is positive constant. 2. Relevant equations I know that in first derivative, vector can change in both magnitude and direction, but I don't have an idea how to differentiate this thing. How would you find acceleration and velocity in latter case? What if b is vector but not constant? By the way,for my second question,I'm studying from University physics by Young and Friedman,and my physics course is kinda more advanced(also first year intro).Our official book is Fundamentals of Mechanics by Irodov(problem book also by Irodov),but it's so devoid of any explanations that it's hopeless to use it for anything else other than reference book.Could you recommend me some equivalent on this level but more pedagogically sound? 3. The attempt at a solution I don't even know how to start.