A particle moves along a line with velocity $v(t)=(t-1)(t-3)^2$ m/s for $0\leq t\leq 3$. On which interval is the speed of the particle increasing?

Core Concept

Speed increases when $v$ and $a$ have the same sign. Here $a(t)=(t-3)(3t-5)$, so $v>0$ and $a>0$ on $(1,\tfrac{5}{3})$. The speed increases throughout this interval.