Single Variable Calculus, Chapter 4, 4.1, Section 4.1, Problem 66

The table below gives the velocity of an object with respect to time

$
\begin{array}{|l|c|c|}
\hline\\
\text{Event} & \text{Time}(s) & \text{Velocity}\displaystyle\left(\frac{\text{ft}}{s}\right)\\
\hline\\
\text{Launch } & 0 & 0\\
\text{Begin roll maneuver} & 10 & 185\\
\text{End roll maneuver} & 15 & 319\\
\text{Throttle to 89%} & 20 & 447\\
\text{Throttle to 67%} & 32 & 742\\
\text{Throttle to 104%} & 59 & 1325\\
\text{Maximum dynamic pressure} & 62 & 1445\\
\text{Solid rocket booster separation} & 125 & 4151\\
\hline
\end{array}
$




a.) Use a graphing device to find the cubic polynomial that best models the velocity of an object.
b.) Find a model for acceleration and use it to estimate the maximum and minimum values of the acceleration during the first 125 seconds.

a.) Based from the values in the graph, we can model the velocity as
$v(t) = 0.0015t^3 - 0.1155t^2 + 24.982 t - 21.269$
Recall that $a(t) = V'(t)$ so the model for acceleration is...
$a(t) = V'(t) = 0.0045t^2 - 0.231t + 24.982$
Let's graph the model for acceleration to estimate the maximum and minimum values


Based from the graph the maximum value $\displaystyle \approx 25 \frac{\text{ft}}{s^2}$ and the minimum value $\displaystyle \approx -4 \frac{\text{ft}}{s^2}$