Chapter 3.3, Problem 15E

$\mathbf{T}\mathbf{i}\mathbf{m}\mathbf{e}$	$\mathbf{V}\mathbf{e}\mathbf{l}\mathbf{o}\mathbf{c}\mathbf{i}\mathbf{t}\mathbf{y}$
$2.0$	$27.9$
$2.5$	$33.8$
$3.0$	$39.7$
$3.5$	$45.6$

a. By calculating differences, show that the data in this table can be modeled by a linear function.

b. What is the slope for the linear function modeling velocity as a function of time? Explain in practical terms the meaning of the slope.

c. Use the data in the table to find the formula for velocity as a linear function of time that is valid over the time period covered in the table.

d. What would your formula from part c given for the velocity of the car at time 0? What does this say about the validity of the linear formula over the initial segment of the experiment? Explain your answers in practical terms.

e. Assume that the linear formula you found in part c is valid from 2 seconds through 5 seconds. The marketing department wants to know from the engineer how to complete the following statement: “This car goes from 0 to 60 mph in _____________ seconds.” How should they fill in the blank?