Mathematics

Problem

A particle moves along a straight line so that its displacement

s

(in metres) at time

t

seconds is given by

s(t)=3t^{2}+2t+1

. (i) Write the expression for the average velocity of the particle over the time interval

[t,\,t+h]

. (ii) Using the limit of the average velocity as

h\to 0

, obtain a formula for the instantaneous velocity

v(t)

. (iii) Calculate the instantaneous velocity at

t=3\;\text{s}