Two cars leave the same intersection at the same moment
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
Two cars leave the same intersection at the same moment. Car A travels due north at a constant speed of 50 km/h, and Car B travels due east at a constant speed of 120 km/h. Let t be the time in hours after the cars leave the intersection, and let s(t) be the straight-line distance (in km) between the two cars at time t.
(a) Express s(t) in terms of t using the given information.
(b) Calculate dtds when t=601 h (10 s). Include appropriate units.
(c) Interpret the sign and magnitude of your answer to part (b) in the context of the motion of the two cars.