  ### Home > APCALC > Chapter 2 > Lesson 2.4.1 > Problem2-138

2-138.

Examine the scenarios below, paying attention to the units.

1. While walking to school, Jaime’s distance from home (in miles) was $s(t)=3t^2$, where $t$ is measured in hours. Sketch a graph of his distance. If it takes Jaime $30$ minutes to walk to school, what is his average velocity? Explain how you got your answer.

This is a distance graph. Time, $t$, should be on the $x$-axis. (It usually is!) And distance, $s(t)$, should be on the $y$-axis. Sketch the graph of $s(t) = 3t^2$.

$\text{Average velocity }=\frac{\Delta \text{distance}}{\Delta \text{time}}$

$\text{Average velocity on }[0,5]=\frac{s(5)-s(0)}{5-0}$

Note that this is the slope of the secant line that connects the points at $t=0$ and $t=5$.

2. While walking home, Jaime walks so that his velocity (in miles per hour) is $v(t) = -2t$, where $t$ is measured in hours. How long does it take him to get home?

Sketch a velocity graph of$v(t) = -2t$. Time, $t$, will be on the $x$-axis. Velocity, $v(t)$, will be on the $y$-axis. How can distance information be found on a velocity graph?