A particle moves along a straight line so that its position at time seconds is given…

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 position at time

t\ge 0

seconds is given by

s(t)=t^{3}\ln(t+1)

meters. (a) Obtain expressions for the velocity

v(t)

and acceleration

a(t)

of the particle in terms of

t

. Present fully simplified results. (b) Evaluate the acceleration at

t=2

seconds, giving an exact value. (c) Determine all values of

t>0

at which the acceleration of the particle is equal to zero. Justify that your answer includes every such time.