Q 2 - Calculus

Question

What was your average distance from the stop sign

from the time that you first saw it to the time that you

came to a stop?

Step-by-Step Solution

Answer

21.67 feet

Step 1: Given

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

s(t) = 3t³ - 12t² - 9t + 54

Step 2: The distance function's average value is provided by,

$$\begin{gathered} =\frac{1}{b-a}{\int }_a^{b}s\left(t\right)dt \\ =\frac{1}{4.6}{\int }_0^{4.6}s\left(t\right)dt \\ =\frac{1}{4.6}{\int }_0^{4.6}\left(3t^3-12t^2-9t+54\right)dt \\ =\frac{1}{4.6}{\left[\frac{3t^4}{4}-12\frac{t^3}{3}-9\frac{t^2}{2}+54t\right]}_0^{4.6} \\ =\frac{1}{4.6}[335.8-389.3-95.2+248.4] \\ =\frac{1}{4.6}[99.7] \\ =21.67 \end{gathered}$$

As a result, the average distance is 21.67 feet.