   Chapter 5.1, Problem 47E

Chapter
Section
Textbook Problem

# Racing cars driven by Chris and Kelly are side by side at the start of a race. The table shows the velocities of each car (in miles per hour) during the first ten seconds of the race. Use the Midpoint Rule to estimate how much farther Kelly travels than Chris does during the first ten seconds. t v C v K 0 0 0 1 20 22 2 32 37 3 46 52 4 54 61 5 62 71 6 69 80 7 75 86 8 81 93 9 86 98 10 90 102

To determine

To use:

The midpoint rule to estimate the distance between the two cars

Explanation

1) Concept:

The area under the velocity curve represents the distance traveled by the car.

Use the midpoint rule to evaluate the area.

2) Midpoint rule

abfx dx=i=1nfxix= x ( f(x1)+fx2++f xn)

where x= b-an and xi is a midpoint of  [xi-1 , xi]

3) Given:

The table that shows velocities of each car (in miles per hour)

4) Calculation:

The area under the velocity curve represents the distance traveled by the car.

The difference of the areas under the curves is thedistance between the cars after 10 seconds.

So we calculate Vk-Vc.

With this data, we can take n = 5, and use the midpoint rule.

To find t,  convert time in hours.

1 second=13600 hours

10 sec =1360h

t=1360-05  =1<

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