Question

The model for the velocity of a shuttle, from liftoff at t = 0 s until the solid rocket boosters were jettisoned at t = 50.2 s, is given by

v(t)=0.001495833t^3−0.089395t^2+18.86t−0.52 (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.

Answer 1

just crank it out. The acceleration is

a(t) = 0.0044875t^2 - 0.17879t + 18.86

a(t) has a max/min when da/dt = 0
da/dt = 0.008975t - 0.17879
da/dt=0 at a=19.9209
a(10.9209) = 17.0792

Since a(t) is a parabola, there is no maximum value, but in the domain [0,50.2], the maximum value is
a(50.2) = 21.1934