MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A cyclist rides along a straight, level road. Over the interval 0≤t≤8 seconds, the cyclist’s velocity v(t) (measured in m\,s−1) satisfies the following description.
• v(t)>0 for 0<t<2 and 5<t<8.
• v(t)=0 at t=2 and again at t=5.
• v(t)<0 for 2<t<5.
Throughout the motion the velocity varies smoothly.
Answer the following, using complete sentences and clear justification.
(a) Identify the times in the interval 0≤t≤8 at which the cyclist is at rest.
(b) For each rest time found in part (a), explain whether the cyclist reverses direction at that moment or merely comes to an instantaneous stop before resuming motion in the same direction. Support your answer by referencing the signs of v(t) immediately before and after each rest time.
(c) State the open sub-intervals of [0,8] on which the cyclist travels to the east (positive direction) and those on which the cyclist travels to the west (negative direction).