Q 3 - Calculus

Question

Use an average rate of change to find your average velocity

during the time that you were trying to stop the

car. (Assume that the average velocity is the average

rate of change of position.)

Step-by-Step Solution

Answer

-0.74 feet per second

Step 1: Given

The function gives the distance from the stop sign (in feet) t seconds after stepping on the brakes is,

$s\left(t\right)=3t^3-12t^2-9t+54$

Step 2: The average rate of change is calculated as follows:

$\begin{array}{rcl}\frac{s\left(b\right)-s\left(a\right)}{b-a}& =& \frac{s(4.6)-s\left(0\right)}{4.6-0}\\ & =& \frac{\left[3(4.6{)}^3-12(4.6{)}^2-9(4.6)+54\right]-\left(54\right)}{4.6-0}\\ & =& \frac{292-254-41.4}{4.6}\\ & =& \frac{-3.4}{4.6}\\ & =& -0.74\end{array}$

As a result, the average speed is -0.74 feet per second.