Question

The loser of the above race had to run an extra 1600 m as terms of a bet. She runs the first 800 m at an average speed of 6 m/s and the next 800 m at an average speed of 8 m/s.

a. What is her total time needed to run 1600 m?
b. What is her average speed?

Answer 1

a. 233.3 s

First, we calculate the time the runner needs to cover the first 800 m:

`t_1 = (d_1)/(v_1)`

where

`d_1 = 800 m`

`v_1 = 6 m/s` is the speed in the first part

Substituting,

`t_1 = (800)/(6)=133.3 s`

Similarly, the time needed to cover the second part was

`t_2 = (d_2)/(v_2)=(800)/(8)=100 s`

So the total time the runner needed to finish the race was:

`t=t_1 + t_2 = 133.3 s + 100 s = 233.3 s`

b. 6.86 m/s

The average speed can be calculated as follows:

`v=(D)/(t)`

where

`D=d_1 + d_2 = 800+800 = 1600 m` is the total length of the race

t = 233.3 s is the time taken

Substituting,

`v=(1600)/(233.3)=6.86 m/s`