(A) We are given the velocity function `v(t)=9t^3+4` and we are asked to find the average velocity over the interval `1<=t<=4` .
The average value of a function f(t) on the interval [a,b] is given by:
So the average velocity is 192.25 units per unit time.
(B) Given the position function `s(t)=3t^2+t` we are asked to find the average velocity of the particle over the interval `1<=t<=4`
Using algebra, the average velocity is the displacement divided by the elapsed time.
s(1)=4 and s(4)=52 so the displacement is 48. The elapsed time is 4-1=3.
The average velocity is `A=48/3=16` units per unit time.