Which of the following statements best explains why the graph of the position…
MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
Which of the following statements best explains why the graph of the position function s(t) for a particle experiencing constant positive acceleration is concave upward for all t?
(a) Since the acceleration is positive, the position is always increasing, and any increasing function must be concave upward.
(b) The velocity remains constant, so s(t) is a straight line and therefore concave upward.
(c) The velocity increases linearly with time, so the slope of s(t) grows at a constant rate, producing upward concavity.
(d) Because the first derivative of s(t) is always positive, the graph must be concave upward for all t.