Step-by-step explanation:
Part 1) What is the slope for section "d" of Mrs. Washington's commute
As the slope for section "d" of Mrs. Washington's commute can be computed by the following formula:
[tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
⇒ [tex]\frac{6 - 0}{32 - 20}=\frac{1}{2}[/tex]
Therefore, the slope for section "d" of Mrs. Washington's commute [tex]\frac{1}{2}=0.5[/tex]
Part 2) What does it mean that the slope is negative in context of the problem?
- The slope is negative in context of the problem means the slope is moving downward from the left.
- In negative slop, the value of x gets increased, while the vale of y gets decreased while in case of positive slop, the value of both x and y get increased.
Part 3) Why are the slopes different over different intervals?
- Slopes are different at different intervals. The reason is that the distance covered in time taken for each part of the given journey are different.
- Also, the speed is different for each interval depending upon the time taken to cover the distance.
Distance-time equation is needed to compute the speed
[tex]Speed\:=\:\frac{distance}{time}\:[/tex]
Let distance be denoted as d, and time be denoted as t
- d = [tex]y_{2} -y_{1}[/tex]
[tex]d=20 - 15 = 5[/tex]
- t = [tex]x_{2} -x_{1}[/tex]
t= 8 - 0 = 8
As
- [tex]Speed\:=\:\frac{distance}{time}\:=\frac{d}{t}[/tex]
[tex]Speed = \frac{5}{8}[/tex]
[tex]Speed = 0.625[/tex]
Hence, the speed in the part 1 would be [tex]0.625[/tex] [tex]ms^{-1}[/tex]
Part 4) How long does it take Mrs. Washington to get home? How did you know this?
- After carefully observing the graph, it sounds clear that Mrs. Washington takes 32 minutes to reach home.
- It can be easily figured out from the graph that it represents the total time taken throughput the complete journey.
Keywords: speed, time
, distance covered
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