# Help with Kinematics problem

## Homework Statement

You nose out another runner to win the 100.000 m dash. If your total time for the race was 11.800 s and you aced out the other runner by .001 s, by how many meters did you win?

vavg=Δx/Δt
v=x/t

## The Attempt at a Solution

v=x/t = 100.00m/11.8s =8.4746m/s.
v=x/t = x=vt = 8.4746m/s(.001s)= .008m

This is the provided answer, however, I tried a different method and got ".0008m" instead, I don't know why. Here's what I did

100m/11.8s= 8.474576271 m/s (this is the average velocity of the winner)
100m/11.8001=8.474504453m/s (this is the average velocity of the loser)

I multiplied the avg velocity of the loser by 11.8, to get the position of the loser as the winner wins.
I got 99.99915255 m. I subtracted this from 100, to see by how many meters the winner won by and I got
.00084745 meters. Don't know why I got an extra 0 in my answer, can anyone please explain? Thanks!

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PeterO
Homework Helper

## Homework Statement

You nose out another runner to win the 100.000 m dash. If your total time for the race was 11.800 s and you aced out the other runner by .001 s, by how many meters did you win?

vavg=Δx/Δt
v=x/t

## The Attempt at a Solution

v=x/t = 100.00m/11.8s =8.4746m/s.
v=x/t = x=vt = 8.4746m/s(.001s)= .008m

This is the provided answer, however, I tried a different method and got ".0008m" instead, I don't know why. Here's what I did

100m/11.8s= 8.474576271 m/s (this is the average velocity of the winner)
100m/11.8001=8.474504453m/s (this is the average velocity of the loser)

I multiplied the avg velocity of the loser by 11.8, to get the position of the loser as the winner wins.
I got 99.99915255 m. I subtracted this from 100, to see by how many meters the winner won by and I got
.00084745 meters. Don't know why I got an extra 0 in my answer, can anyone please explain? Thanks!
The two values in red do not match. Second should be 11.801