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Acceleration Rate of Change of Homer Simpson

Homer Simpson lies directly in the path of the flame-spewing juggernaut, with only the meager acceleration of the family station wagon standing between him and utter destruction.

Assume Homer's velocity (in feet per second) is given by the equation:
V(t)=t^3-4t^2-t-x+1 ,

where t is measured in seconds and . Answer the following questions based on the given information, accurate to the thousandths place.

(a) Is Homer traveling backwards at any time during the first 7 seconds of his escape attempt? If so, during what time interval(s) is the gear shift in reverse?

(b) What is Homer's average velocity from t = 2 to t = 5?

(c) At what time(s) does Homer change from accelerating to decelerating, or vice versa?

Solution Preview

Please see the attached file.

Professor Frink never anticipated Truckasaurus getting loose, but then again, he never foresaw the obvious dangers in reanimating the corpse of his long-dead father. Frinkie's not one for long-term planning. Anyway, Homer Simpson lies directly in the path of the flame-spewing juggernaut, with only the meager acceleration of the family station wagon standing between him and utter destruction.

Assume Homer's velocity (in feet per second) is given by the ...

Solution Summary

This is a calculus problem involving velocity and acceleration rate of change of Homer Simpson.

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