At time , the velocity of a particle changes from positive to negative, and . Which…
MATHEMATICS · Single correct · A Level · Mathematics · Kinematics · Kinematics
Problem
At time t=c, the velocity of a particle changes from positive to negative, and f′′(c)<0. Which conclusion about the particle at t=c is most justified?
(a) The particle reaches a local minimum position because its velocity changes sign from positive to negative while its acceleration is negative.
(b) The particle’s speed is increasing because its velocity and acceleration have opposite signs.
(c) The particle reaches a local maximum position because its velocity changes from positive to negative and f′′(c)<0.
(d) The particle is slowing down because its acceleration is negative while its velocity is positive just before t=c.