An object moving along a horizontal line has velocity v(t)=t^ 3 -6t^ 2 +9t for seconds
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
An object moving along a horizontal line has velocity
v(t)=t3−6t2+9t
for 0≤t≤5 seconds, where t is measured in seconds and v in meters per second.
(a) Find the object’s acceleration a(t) for 0≤t≤5.
(b) Determine all open time intervals on (0,5) during which the object’s speed is increasing and all intervals during which its speed is decreasing. Fully justify your answer.
(c) At what time(s) in (0,5) does the object attain a local maximum value of speed? At what time(s) does it attain a local minimum value of speed? Justify your conclusions.