A sprinter’s position (in meters) along a straight track is shown as a smooth curve…
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A sprinter’s position s (in meters) along a straight track is shown as a smooth curve on a time–position graph. Grid lines mark every 10 seconds horizontally and every 5 meters vertically. The point Q on the curve at t=40 s has coordinates (40,60). The tangent line drawn at Q intersects the vertical grid line at t=30 s at the point (30,15).
Use this information to analyze the runner’s motion.
(a) Estimate the instantaneous velocity of the sprinter at t=40 s. Show your calculation and include correct units.
(b) The average velocity of the sprinter on the interval [30,50] is approximately 2.3 m/s. Compare this average velocity to the instantaneous velocity you found in part (a) and interpret what this indicates about the sprinter’s change of speed over that time period.