A particle moves along a straight line so that its displacement (in meters) from the…

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A particle moves along a straight line so that its displacement (in meters) from the origin at time

t

seconds is given by

s(t)=k t^{5/2}

, where

k

is a positive constant and

t\ge 0

. (a) Determine the particle's acceleration

a(t)

as a function of

t

and

k

. (b) The jerk is defined as the third derivative of displacement with respect to time. Find an explicit expression for the jerk

j(t)

. (c) For

k=3

, evaluate

j(4)

. Include appropriate units in your final answer and interpret its physical meaning in one complete sentence.