A small cart travels a distance of $0.1t^{3}$ feet in the first $t$ seconds of travel for $0 ≤ t ≤ 10$.

1. Find its velocity after $5$ seconds.

   Hint (a):

   First find the slope function.

   $\lim\limits_{ h \to 0} \frac{f(t+h)-f(t)}{t+h-t}$

   Then find $d^\prime \left(5\right)$.

   Answer (a):

   $7.5 \frac{\text{ft}}{\text{sec}}$

2. Find its velocity after $t$ seconds.

   Hint (b):

   This is the slope function found above.