Mathematica Tool 1

This Mathematica notebook is designed to be used with Checkpoint 2 in Section 7.1.2

Here is a copy of Figure 2 from 7.1.2. The units for velocity v are miles per hour and for time t are  minutes.

The following list contains the velocites v in miles per hour at every half-minute except 4.5 minutes (10th entry) and 10.5 minutes (22 entry). Estimate these velocities from the graph and enter them in the list (replace "???") before trying to execute the next command.

v={0,8.5,14.0,15.0,15.0,15.0,18.2,24.5,30.0,"???",31.0,30.7,31.0,31.5,30.0,25.1,20.0,17.7,17.0,16.2,15.0,"???",13.0,12.7,11.0,6.4,0};

Enter a value for the constant c below so that V  represents the velocity in miles per minute.

c= "???";
V=c v

Check your value of c by observing (in Table 1) that at time t=2 minutes, the velocity should be .25 miles per minute

Now calculate the estimated distance traveled. In each half-minute interval, we assume the velocity is constant as determined at the start of the interval, so the distance is the starting velocity times (1/2) minute. We add these up to get the total distance (in miles).

TotalDistance=Sum[((V[[i]])/2),{i,1,Length[V]}]

Now we divide by the total time (13 minutes) to get the average speed.

(TotalDistance/13)

Finally. we convert back to miles per hour.

%/c