Question

A bicyclist travels the

Dicyclist travels the first 800 m of a trip with a
of 10 m/s, the next 500 m with an average
ed of 5 m/s and the final 1200 m at a speed of
13 m/s. Find the average speed of the bicyclist for
this trip.

Answer 1

Answer: 9.18 m/s

Step-by-step explanation:

We have a straight line where the bicyclist travels a total distance
`D`, which is divided into three segments:

`D=d1+d2+d3` (1)

On the other hand, we know speed is defined as:

`S=(d)/(t)` (2)

Where
`t` is the time, which can be isolated from (2):

`t=(d)/(S)` (3)

Now, for the first segment
`d1=800 m` the bicyclist has a speed
`S_(1)=10 m/s`, using equation (3):

`t_(1)=(d1)/(S_(1))` (4)

`t_(1)=(800 m)/(10 m/s)` (5)

`t_(1)=80 s` (6) This is the time it takes to travel the first segment

For the second segment
`d2=500 m` the bicyclist has a speed
`S_(2)=5 m/s`, hence:

`t_(2)=(d)/(S_(2))` (7)

`t_(2)=(500 m)/(5m/s)` (8)

`t_(2)=100 s` (9) This is the time it takes to travel the second segment

For the third segment
`d3=1200 m` the bicyclist has a speed
`S_(3)=13 m/s`, hence:

`t_(3)=(d)/(S_(3))` (10)

`t_(3)=(1200 m)/(13m/s)` (11)

`t_(3)=92.3 s` (12) This is the time it takes to travel the third segment

Having these values we can calculate the bicyclist's average speed
`S_(ave)`:

`S_(ave)=(d1 + d2 +d3)/(t_(1) + t_(2) +t_(3)) <strong>(13)</strong> </p><p></p><p>[tex]S_(ave)=(800 m + 500m + 1200 m)/(80 s +100 s + 92.30 s)` (14)

Finally:

`S_(ave)=9.18 m/s`