A train departs a station at time minutes and moves along a straight track
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A train departs a station at time t=0 minutes and moves along a straight track. Its position relative to the station is modeled for 0≤t≤10 by
s(t)=150ln(5t+1)−25t,
where s(t) is measured in meters.
(a) Derive an explicit formula for the train’s velocity v(t).
(b) Determine all times in the interval 0≤t≤10 at which the train is momentarily at rest.
(c) Compute the total distance traveled by the train during the first 10 minutes.
(d) Explain, with justification based on your work, whether the train ever reverses direction on the interval 0≤t≤10. Cite specific features of the velocity function in your reasoning.