MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Two students, Alex and Bree, are analyzing the motion of a particle whose velocity for t≥0 is v(t)=2t+1 meters per second.
• Alex concludes the position function is sA(t)=t2+t+4.
• Bree concludes the position function is sB(t)=t2+t−3.
Suppose it is known that the particle is at the origin when t=0; that is, s(0)=0.
(a) Explain, without performing any numerical calculations, why sA(t) and sB(t) cannot both represent the same physical motion under the given initial condition.
(b) Determine which student’s position function (if either) is consistent with the stated initial condition, and justify your conclusion.
(c) For the correct position function, compute the particle’s position at t=5 seconds and interpret the result.