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Chapter 4: Q 4 (page 400)

Find your average velocity from the oak tree to the

stop sign anotherway, as follows: Differentiate the formula

for position to get a formula v(t) for your velocity,

in feet per second, t seconds after hitting the brakes.

Then use a definite integral to find the average velocity

during the time that you were trying to stop the car.

(Your final answer should of course be the same as the

average velocity you found in the last part)

Short Answer

Expert verified

-0.74 feet per second

Step by step solution

01

Given

The function, gives the distance from the stop sign (in feet) t seconds after stepping on the brakes is

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

02

By differentiation method

s(t)=3t3-12t2-9t+54ds(t)dt=9t2-24t-9v(t)=9t2-24t-9鈭�0vv(t)dt=鈭�04.69t2-24t-9dt鈭�0vv(t)dt=9t3304.6-24t2204.6-9t104.6v(t)=9t3304.6-24t2204.6-9t104.6v(t)=292-254-41.4v(t)=-3.4Thisisthevelocityonthetimeinterval[0,4.6].Hence,theaveragecanbecalculatedby-3.44.6.Asaresult,theaveragespeedis-0.74feetpersecond.

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Most popular questions from this chapter

Given formula for the areas of each of the following geometric figures

a) area of circle with radius r

b) a semicircle of radius r

c) a right triangle with legs of lengths a and b

d) a triangle with base b and altitude h

e) a rectangle with sides of lengths w and l

f) a trapezoid with width w and heighth1,h2

Without using absolute values, how many definite integrals would we need in order to calculate the absolute area between f(x) = sin x and the x-axis on [-蟺2,2蟺]?

Will the absolute area be positive or negative, and why? Will the signed area will be positive or negative, and why?

Determine which of the limit of sums in Exercises 47鈥�52 are infinite and which are finite. For each limit of sums that is finite, compute its value

limn鈫�鈭�鈭�k=1nk3n4+n+1

Construct examples of the thing(s) described in the following. Try to find examples that are different than any in the reading.

(a) A function f for which the signed area between f and the x-axis on [0, 4] is zero, and a different function g for which the absolute area between g and the x-axis on [0, 4] is zero.

(b) A function f whose signed area on [0, 5] is less than its signed area on [0, 3].

(c) A function f whose average value on [鈭�1, 6] is negative while its average rate of change on the same interval is positive.

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).

鈭�x2x3+15dx.
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