Can anyone finally help me with this Calculus proof?
Using derivatives a = dv/dt, v = ds/dt and |v| = speed, show that if an object is moving on a straight line, then its speed is increasing when its velocity v and its acceleration a have the same sign and its speed is decreasing when v and a have opposite sign.
I’m taking the first class in Calculus and this problem is from applications of antidifferentiation. My teacher says that no fancy Trigonometry is necessary. There is a hint: If |v| = S, when v > 0, S = v and dS/dt = dv/dt = a. When v < 0, S = - v and dS/dt = - dv/dt = - a...but I'm not seeing how to do this.