A particle moves along a straight line and its displacement at time seconds is…
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A particle moves along a straight line and its displacement at time t seconds is denoted by s(t) metres.
(i) Define the terms velocity and acceleration in the context of this motion, expressing each in terms of derivatives of s(t).
(ii) If at a certain instant the velocity of the particle is positive while its acceleration is negative, explain whether the speed of the particle is increasing or decreasing at that instant. Justify your answer mathematically.
(iii) At time t=t0 the particle has zero velocity but positive acceleration. State what can be inferred about the motion of the particle immediately after t0 and give a brief reason.