Mathematics

Problem

For

0\le t\le4

, the position of a point mass moving along a straight track is given by

s(t)=4t^{4}-16t^{3}+6t^{2}+5,

where

s

is measured in meters and

t

in seconds. a. Calculate the instantaneous velocity of the point mass at

t=1\text{ s}

. b. Calculate the instantaneous acceleration of the point mass at

t=1\text{ s}

. c. Determine the average velocity of the point mass on the interval

0\le t\le2

and compare it with your answer from part (a), commenting on the motion of the point mass around

t=1\text{ s}