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Chapter 4: Q. 1 TF (page 388)

Just as you are driving past the big oak tree on Main Street, you notice a new

stop sign 54 feet ahead of you. You slam on your brakes and end up coming to a full stop exactly at the stop sign.

Suppose that your distance from the stop sign (in feet) tseconds after stepping on the brakes is given by the functions(t)=3t3鈭�12t2鈭�9t+54. By working through the following five problems you will see another argument that the distance travelled is related to the signed area under the velocity curve; this set of problems previews the Second Fundamental Theorem of Calculus, which we will see in Section 4.7.

How long did it take you to come to a full stop?

Short Answer

Expert verified

4.6seconds will take tocome to a full stop.

Step by step solution

01

Step 1. Given information

The given function for the distance from the stop sign is:

s(t)=3t3鈭�12t2鈭�9t+54

02

Step 2. Time took to a full stop the car 

A stop sign is noticed 54feet before and the car stops at the sign.

Substitute 54for the function value in the function s(t)and solve the equation for t.

role="math" localid="1654125190162" s(t)=3t3鈭�12t2鈭�9t+5454=3t3鈭�12t2鈭�9t+543t3鈭�12t2鈭�9t=03t(t-4.6)(t+0.6)=0t=0,-0.6,4.6

as t>0

so t=4.6

4.6 seconds will take to stop the car.

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