Consider the velocity function The particle starts at the origin at and moves along…
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
Consider the velocity function
v(t)=(t−2)2(t−6)(meters per second),0≤t≤8.
The particle starts at the origin at t=0 and moves along the x–axis.
(a) Identify the intervals on 0≤t≤8 for which v(t) is positive and for which v(t) is negative.
(b) Explain how the sign of v(t) on an interval determines whether the particle’s position function is increasing or decreasing on that interval.
(c) State all times in 0≤t≤8 at which the particle changes direction and justify your answer fully.
(d) Without evaluating any integrals, decide whether the magnitude of the particle’s displacement on [0,2] is greater than, less than, or equal to the magnitude on [2,6]. Support your conclusion with reasoning based on the behavior of v(t).