The position of a particle moving along a straight line is given by metres

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

Problem

The position of a particle moving along a straight line is given by

s(t)=3t^{3}-12t^{2}+9t+5

metres, where

t

is the time in seconds

(1\le t\le 3)

. (i) Determine the average velocity of the particle during the time interval

[1,3]

. (ii) Find the expression for the instantaneous velocity

v(t)

. (iii) Calculate all values of

t

in the open interval

(1,3)

for which the instantaneous velocity equals the average velocity obtained in part (i). (iv) Compute the acceleration of the particle at each value of

t

found in part (iii) and state whether the particle is speeding up or slowing down at that instant.