### Home > CALC > Chapter 6 > Lesson 6.2.2 > Problem6-75

6-75.

While riding his bike to a pond, Steven's distance in miles was modeled by $s(t)$ below. If the lake was $9$ miles away and if $t$ is measured in hours:

$s(t) = t^3 − 3t^2 + 3t$

1. What was Steven's maximum velocity during the trip? When did it occur?

$v(t) = 3t^2 − 6t + 3 = 3(t − 1)^2$

Visualize $v(t)$. It is a concave up parabola; therefore there cannot be a local maximum. But Steven didn't ride his bicycle forever! You can still find the maximum velocity during the time interval when Steven was on his bike... Check the Endpoints!

2. Did Steven ever stop during the trip? Justify your conclusion analytically.

Does $v(t)$ ever equal $0$ during the time interval of Steven's bike ride?

3. What was Steven's average velocity?

Average Velocity $=\frac{\text{displacement}}{\text{time}}$