A University of Rochester student decided to depart from Earth after his graduation to find work on Mars. Before building a shuttle, he conducted careful calculations. A model for the velocity of the shuttle, from liftoff at t = 0 s until the solid rocket boosters were jettisoned at t = 67.8929589270746 s, is given by

Question

A University of Rochester student decided to depart from Earth after his graduation to find work on Mars. Before building a shuttle, he conducted careful calculations. A model for the velocity of the shuttle, from liftoff at t = 0 s until the solid rocket boosters were jettisoned at t = 67.8929589270746 s, is given by
 v(t)=0.00198833333333333t 3 −0.085875t 2 +26.23t−1.34 (in feet per second).
Using this model, estimate the absolute maximum value and absolute minimum value of the ACCELERATION  of the shuttle between liftoff and the jettisoning of the boosters.

Steve · Accepted Answer

just plug and chug:

v=0.00198833333333333t^3 −0.085875t^2 +26.23t−1.34
since acceleration is v',
a = 0.005965t^2 - 0.17175t + 26.23
That's just a parabola opening up, with vertex at (14.3965,24.9937)

So, the minimum acceleration is 25, and the maximum will be at either t=0 or t=67...

I expect it will be the latter. Plug in that for t and evaluate v(t) there.