A small cart travels a distance of $0.1t^{3}$ feet in the first $t$ seconds of travel for $0\le t\le10$.

1. What is the cart’s velocity when $t = 5$ seconds?

   Step (a):

   $v(5)= \lim \limits_{ h \to 0} \frac{0.1(5+h)^3-0.1(5^3)}{h}$

2. What is the cart’s velocity at any time, $t$ seconds?

   Step (b):

   $v(t)= \lim \limits_{ h \to 0} \frac{0.1(t+h)^3-0.1(t^3)}{h}$