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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 Summary

This is a calculus problem involving velocity and acceleration.