The displacement (in metres) of a particle at time seconds is given by s(t)=2t^ 4…

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

Problem

The displacement

s

(in metres) of a particle at time

t

seconds is given by

s(t)=2t^{4}-3t^{3}+4t.

Answer the following: (i) Find expressions for the velocity

v(t)

and the acceleration

a(t)

. (ii) Calculate the acceleration at

t=1\text{ s}

and

t=2\text{ s}

. (iii) For

0\le t\le3

, determine the interval(s) during which the particle is speeding up and the interval(s) during which it is slowing down.