The velocity of a particle moving along a coordinate line is given for all real by…
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
The velocity of a particle moving along a coordinate line is given for all real t by v(t)=(t−1)(t−3) meters per second. The particle’s position function s(t) satisfies s(0)=2.
Assume t=0 corresponds to the instant the particle passes through position s=2.
(a) Determine the explicit formula for s(t).
(b) Find all times t>0 at which the particle is 8 meters from the origin; that is, solve s(t)=8 for t>0.
(c) Determine the total distance traveled by the particle during the time interval 0≤t≤4, and explain your reasoning carefully.