MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A particle moves along a straight line, and its velocity at time t seconds is given by v(t)=2(t−3) meters per second for 0≤t≤6.
(a) Identify the time intervals on which the particle moves to the right and the time intervals on which it moves to the left. Provide reasoning based on the sign of v(t).
(b) Without evaluating any definite integrals, determine whether the particle’s displacement over the interval 0≤t≤6 is positive, negative, or zero. Justify your answer in terms of areas above and below the t-axis on the velocity graph.
(c) Explain the difference between displacement and total distance traveled for this motion, and state which of the two quantities is larger over 0≤t≤6. Support your conclusion with reasoning tied to the behavior of v(t).