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 table gives the velocity data for the shuttle between liftoff and the jettisoning of the solid rocket boosters.




(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 ε [0, 125]. 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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Velocity (ft/s) Event Time (s) Launch Begin roll maneuver End roll maneuver 185 10 15 319 Throttle to 89% 20 447 32 Throttle to 67% 742 Throttle to 104% 59 1325 Maximum dynamic pressure Solid rocket booster separation 62 1445 125 4151