Inverting v(t) = dx/dt, we have the change of position between two times, to and tf:?(??)??(??)=??????(?)d?x(tf)?x(to)=?totfv(t)dtThe average velocity = [x(tf) - x(to)]/[tf - to]. We also use the arithmetic mean (the usual mean). You may take the time and distance units as meter and second, for the numbers.Use this velocity function: v(t) = 7 + 4t. Calculate the mean of v(0) and v(5).Calculate the change in position, with to = 0 and tf = 5.Calculate the average velocity.Repeat calculations 1-3 with this velocity: v(t) = 11/(6-t), with to = 0 and tf = 5 still.For the first velocity function, if calculations 1 and 3 are different, try again. They should be different for the second velocity function.

Description This problem is intended as further examples of mean and average. We use two different types of average. An object's position is a function of time: x(t) in one dimension. Its velocity is v(t) = dx/dt. Various plots of position and position against time are shown. The most relevant plot is the fourth, the bottom-right. Time is on the horizontal axis, and position on the vertical axis -- the units are arbitrary in the plot. ' 4" ' /\""