A particle moves along a straight line with velocity given by for
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A particle moves along a straight line with velocity given by v(t)=3t2−12t+9 for 0≤t≤5, where t is measured in seconds and v in meters per second. At time t=2 s the particle is observed to be 5 m to the right of the origin.
Answer the following questions. Emphasis is placed on clear explanation and correct use of mathematical vocabulary.
(a) Describe on which sub-intervals of 0≤t≤5 the particle moves to the right and on which it moves to the left. Justify your answer by referencing properties of the velocity function.
(b) Explain, without performing detailed calculations, why any antiderivative of v(t) must include an additive constant and how the given position at t=2 can be used to determine its value.
(c) Let s(t) denote the particle’s position. State the mathematical condition that s(t) must satisfy at t=2 and describe in words its physical meaning in the context of the motion.