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Chapter 4: Q. 2 TF (page 388)

What was your average distance from the stop sign from the time that you first saw it to the time that you came to a stop?

Short Answer

Expert verified

The solution is21.67feet.

Step by step solution

01

Step 1. Given information

The distance from the stop sign (in feet) seconds after stepping on the breaks is given by the function,

s(t)=3t3-12t2-9t+54

02

Step 2. Calculation

The average value of the distance function is given by,

=1b-a鈭�abs(t)dt=14.6鈭�04.6s(t)dt=14.6鈭�04.6(3t3-12t2-9t+54)dt=14.6[3t44-12t33-9t22+54t]04.6 =14.6[335.8-389.3-95.2+248.4]=14.6[99.7]=21.67

Thus, the average distance is21.67feet.

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Use integration formulas to solve each integral in Exercises 21鈥�62. You may have to use algebra, educated guess- and- check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating. (Hint for Exercise 54: tanx=sinxcosx).

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