A University of Rochester student decided to depart from Earth after his graduat

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 = 57.5 s, is given by

(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.

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 = 57.5 s, is given by v(t) = 0.001500000 t^3- 0.08 t^2 + 16.02 t - 2.37 (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.

Explanation / Answer

v(t)=0.001500000t3-0.08t2+16.02t-2.37

acceleration will be derivative of velocity

hence a=dv/dt=0.0045t2-0.16t+16.02

at t=0,a=16.02

now the maximum acceleration will be at endpoint i.e.t=57.5s

so at t=57.5,a=21.698

for minimum acceleration,a'(t)=   0.009t-0.16<0

t<17.77

mimimum acceleration will be at t=17.77,a(t)=14.597

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