A particle moves along a straight line so that its velocity (in meters per second) at…
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
A particle moves along a straight line so that its velocity (in meters per second) at time t seconds is v(t)=6t−4 for t≥0. At time t=1, the particle is located 10 meters to the right of the origin.
(a) Find an expression for the particle’s position s(t), in meters, for t≥0.
(b) Determine the time at which the particle crosses the origin (s(t)=0). Provide exact value(s) and justify why your answer satisfies the given initial condition.
(c) Compute the total displacement of the particle during the first 4 seconds and interpret your result in the context of the motion.