On May 7, 1992, the space shuttle Endeavour was launched on mission STS-49, the purpose of which was to install a new perigee kick motor in an Intelsat communications satellite. The following table gives the velocity data for the shuttle between liftoff and the jettisoning of the solid rocket boosters.
Event
Time (s)
Velocity (ft/s)
Launch
0
Begin roll maneuver
10
185
End roll maneuver
15
319
Throttle to 89%
20
447
Throttle to 67%
32
742
Throttle to 104%
59
1325
Maximum dynamic pressure
62
1445
Solid rocket booster separation
125
4151
(a) Use a graphing calculator or computer to find the cubic polynomial that best models the velocity of the shuttle for the time interval t . Then graph this polynomial.
(b) Find a model for the acceleration of the shuttle and use it to estimate the maximum and minimum values of the acceleration during the first 125 seconds.
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