For , the velocity of a particle moving along a straight track is given by meters per…
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
For 0≤t≤8, the velocity of a particle moving along a straight track is given by v(t)=5cos(4πt) meters per second.
(a) Solve v(t)=0 on the interval 0≤t≤8, and interpret the significance of each solution for the particle’s motion.
(b) Determine the particle’s displacement, in meters, from t=0 to t=8.
(c) Compute the total distance, in meters, traveled by the particle on the interval 0≤t≤8. Show how you organize your work to account for any changes in direction.
(d) Explain why the relationship between the answers in parts (b) and (c) must hold for any continuous velocity function symmetric about its average value on the interval.