Answer: 9.18 m/s
Explanation:
We have a straight line where the bicyclist travels a total distance [tex]D[/tex], which is divided into three segments:
[tex]D=d1+d2+d3[/tex] (1)
On the other hand, we know speed is defined as:
[tex]S=\frac{d}{t}[/tex] (2)
Where [tex]t[/tex] is the time, which can be isolated from (2):
[tex]t=\frac{d}{S}[/tex] (3)
Now, for the first segment [tex]d1=800 m[/tex] the bicyclist has a speed [tex]S_{1}=10 m/s[/tex], using equation (3):
[tex]t_{1}=\frac{d1}{S_{1}}[/tex] (4)
[tex]t_{1}=\frac{800 m}{10 m/s}[/tex] (5)
[tex]t_{1}=80 s[/tex] (6) This is the time it takes to travel the first segment
For the second segment [tex]d2=500 m[/tex] the bicyclist has a speed [tex]S_{2}=5 m/s[/tex], hence:
[tex]t_{2}=\frac{d}{S_{2}}[/tex] (7)
[tex]t_{2}=\frac{500 m}{5m/s}[/tex] (8)
[tex]t_{2}=100 s[/tex] (9) This is the time it takes to travel the second segment
For the third segment [tex]d3=1200 m[/tex] the bicyclist has a speed [tex]S_{3}=13 m/s[/tex], hence:
[tex]t_{3}=\frac{d}{S_{3}}[/tex] (10)
[tex]t_{3}=\frac{1200 m}{13m/s}[/tex] (11)
[tex]t_{3}=92.3 s[/tex] (12) This is the time it takes to travel the third segment
Having these values we can calculate the bicyclist's average speed [tex]S_{ave}[/tex]:
[tex]S_{ave}=\frac{d1 + d2 +d3}{t_{1} + t_{2} +t_{3}} (13)
[tex]S_{ave}=\frac{800 m + 500m + 1200 m}{80 s +100 s + 92.30 s}[/tex] (14)
Finally:
[tex]S_{ave}=9.18 m/s[/tex]
