Chapter 7.3, Problem 35E

Distance When data are given in tabular form, you may need to vary the size of the interval to calculate the area under the curve. The next two exercises include data from Car and Driver magazine. To estimate the total distance travelled by the car (in feet) during the time it took to reach its maximum velocity, estimate the area under the velocity versus time graph, as in the previous two exercises. Use the left endpoint for each time travel ( the velocity at the beginning of that interval ) and then the right endpoint (the velocity at the end of the interval ). Finally, average the two answers together. Calculating and adding up the areas of the rectangles is most easily done on a spreadsheet or graphing calculator. As in the previous two exercises, you will need to multiply by a conversion factor of $\text{5280/3600}=\text{22/15}$, since the velocities are given in miles per hour, but the time is in seconds, and we want the answer in feet. Source : Car and Driver.

Estimate the distance traveled by the Chevrolet Malibu Maxx SS, using the table below.

Acceleration	Seconds
Zero to $30mph$	$2.4$
$40mph$	$3.5$
$50mph$	$5.1$
$60mph$	$6.9$
$70mph$	$8.9$
$80mph$	$11.2$
$90mph$	$14.9$
$100mph$	$19.2$
$110mph$	$24.4$