Mathematics

Problem

A particle moves along a straight line so that its position, in meters from a fixed origin, is given by

s(t)=2t^{3}-15t^{2}+24t+5, \qquad 0\le t\le 6,

where

t

is measured in seconds. a. Calculate the average velocity of the particle on the interval

1\le t\le 4

. State units clearly. b. Determine the instantaneous velocity of the particle at

t=4

seconds. c. Discuss whether the particle is speeding up or slowing down at

t=4

seconds, supporting your answer with appropriate reasoning.