How speed changes

Speed is |v|. When v 0, speed increases if velocity and acceleration have the same sign and decreases if they have opposite signs. Why: with v>0, speed equals v, so its derivative is a. With v<0, speed equals -v, so its derivative is -a. Thus the sign of va determines the trend. Method: calculate a; locate zeros of both v and a in the time domain; make a sign table on the resulting intervals; interpret va. Check both sides of every zero. For v=t-2 on 0 <= t 4, a=1. Speed decreases before 2 s because v<0, and increases afterwards because v>0. Check: zero acceleration is only a candidate for a change in trend. For v=(t-1)3+2, acceleration is zero at 1 but positive on both sides, and positive velocity keeps increasing.