A particle moving along a line has acceleration given by meters per second squared for
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
A particle moving along a line has acceleration given by a(t)=−9+3t meters per second squared for 0≤t≤6. At time t=0 seconds the particle’s velocity is 12 meters per second and its position is 5 meters.
(a) Determine explicit formulas for the velocity v(t) and the position s(t) of the particle for 0≤t≤6.
(b) Find the time t at which the velocity attains an extreme value on the given interval. Classify this extreme value as a maximum or minimum and justify your answer.
(c) Identify all intervals on 0<t<6 during which the particle is speeding up and all intervals during which it is slowing down. Explain how you used the relationship between v and a to reach your conclusions.
(d) Determine the particle’s maximum displacement from its initial position during 0≤t≤6. Support your answer with appropriate reasoning based on your expressions for s, v, and a. State your result with units.