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 â0.085875t 2 +26.23tâ1.34 (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.
v(t)=0.00198833333333333t 3 â0.085875t 2 +26.23tâ1.34 (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.
Answers
Steve
just plug and chug:
v=0.00198833333333333t^3 â0.085875t^2 +26.23tâ1.34
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.
v=0.00198833333333333t^3 â0.085875t^2 +26.23tâ1.34
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.