An object is projected vertically upward from ground level with velocity (in m/s)…
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
An object is projected vertically upward from ground level with velocity (in m/s) modeled by v(t)=40e−0.1t−9.8t, where t is measured in seconds. Positive velocity corresponds to upward motion.
(a) Determine the acceleration function a(t) and include units.
(b) Find the exact time t>0 at which the acceleration equals −14m/s2. Round your answer to the nearest hundredth of a second.
(c) Determine the minimum (most negative) value of the acceleration and state when it occurs. Provide justification.
(d) Interpret the long-term behaviour of a(t) as t→∞ in the context of forces acting on the object.