### Home > PC > Chapter 9 > Lesson 9.3.5 > Problem9-155

9-155.

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.

First find the slope function.

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

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

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

2. Find its velocity after $t$ seconds.

This is the slope function found above.