## Wednesday, September 23, 2009

### Per4: Usain Bolt's 2008 Race Analysis

Today in class, we examined the concept of an average rate of change by analyzing different intervals of Usain Bolt's 100m World Record run at the 2008 Beijing Olympics. We used data from the article, "Bolt's 9.69s. Analysis of speed during the world record. How fast did Bolt run?"

Please add a comment regarding the race interval that your group was responsible for. Include the calculation that you used to determine the average velocity. This may be a good opportunity to try out the sitmo link on the right-hand side of the blog.)

(You can view the video in the post below.)

1. Interval: 10m - 20m
Distance Travelled: 10m
Time Elapsed: 2.87s - 1.85s = 1.02s

V = d2 - d1/t2 - t1
= 20 - 10/2.87 - 1.85
= 9.8m/s

2. INTERVAL : 20 - 30 m
DISTANCE TRAVELLED : 10 m
TIME ELAPSED : 0.91 s

v = d2 - d1 / t2 - t1
= 10m / 0.91s
=(approximately) 11m/s

3. Interval: 10 to 20 m
Distance travelled: 10m
Time elapsed: 1.02 sec

V= d2-d1/t2-t1
= (20-10)/(2.87-1.85)
= (10m)/(1.02s)
= 9.80 m/s

4. Interval: 80 to 90 m
Distance traveled: 10m
Time elapsed: 0.83s

v = d2-d1/t2-t1
= (90-80)/(8.79.-7.96)
= (10m)/(0.83s)
= 12.05 m/s

5. Interval: 70-80m
Distance Traveled: 80m-70m = 10m
Time Elapsed: 7.96-7.14 = 0.82s

Average Velocity = d2-d1/t2-t1
= 10m/0.82s
= 12.2m/s

6. Interval: 30 to 40 m
Distance traveled: 10m
Time elapsed: 0.87s

v = d2-d1/t2-t1
= (40-30)/(4.65-3.78)
= (10m)/(0.87s)
= 11.49 m/s

7. Interval: 80 m to 90 m
Distance travelled: 10 m

Time at 90 m: 8.79 s
Time at 80 m: 7.96 s
Time elapsed: 0.83 s

V = (delta d)/(delta t)
V = 10m/0.83s
V = 12.05 m/s

8. Interval: 60 m to 70 m
Distance Travelled: 70 m - 60 m = 10 m
Time Elapsed: 7.14 s - 6.32 s = 0.82 s

AV=delta d/ delta t
=d2 - d1/t2 - t1
=(70 m - 60 m)/(7.14 s - 6.32 s)
=(10 m)/(0.82 s)
=12.2 m/s

9. Interval: 70m to 80m
Distance travelled: d2-d1=10m
Time elasped: t2-t1= 7.14-6.32=0.82

Average velocity=d2-d1/t2-t1
=10/0.82
=12.2m/s

10. Interval: 70-80m
Distance Traveled: 80m-70m = 10m
Time Elapsed: 7.96-7.14 = 0.82s

Average Velocity = d2-d1/t2-t1
= 10m/0.82s
= 12.2m/s

11. Interval: 50 to 60

Distance Traveled:
= d2-d1
= 60m-50m
= 10 m

Time Elapsed: t2
=t2-t1
= 6.32s-5.5s
= 0.82 s

Average Velocity
= d2-d1 / t2-t1
= 10m/0.82s
= 12.2m/s

12. interval: 0m- 10m

change in distance (m)= d2-d1
= 10m-0m
= 10m

change in time (s)= t2-t1
= 1.85s-0s
= 1.85 seconds

average velocity (m/s)= change in distance/change in time
= 10m/1.85s
= approximately 5.4 m/s

13. Interval-> 0-10 m

d= m t= s

(t1, d1) = (0,0) (t2, d2) = (1.85, 10)

AROC [0,10} = d2-d1
t2-t1

= 10m-0m
1.85s-0s
= approx. 5.4 m/s

Therefore, Bolt's average velocity for the interval 0-10 m is 5.4m/s

14. Interval= 20m-30m
t1= 2.87s
t2= 3.78s
d1= 20m
d2= 30m

=30-20/3.78-2.87
=10/0.91
=11m/s

15. This comment has been removed by the author.

16. Interval: 20m - 30m
Distance Travelled: 10m
Time Elapsed: 3.78s - 2.87s = 0.91 s

Average Velocity = (d2 - d1) \ (t2 - t1)
= 10m \ 0.91s
= 11.0 m/s

Therefore, the average velocity is approx. 11.0 m/s.

17. Interval: 40m-50m
Distance Traveled: 10m
Time Elapsed:
= t2-t1
= 5.5s-4.65s
= 0.85s

Average Velocity:
= d2-d1 / t2-t1
= 10m/0.85s
= 11.8m/s

18. Interval: 90m-100m

Distance Travelled: Δd = d2-d1
= 100 m-90 m
= 10 m

Time Elapsed: Δt = t2-t1
= 9.69 s-8.79 s
= 0.9 s

Average Velocity = Δd/Δt
= 10 m/0.9 s
= 11.1 m/s(rounded to the nearest tenth)

.: The average velocity is approximately 11.1 m/s.

19. Interval (m) : 20 - 30 m
Distance Travelled : d2-d1= 10 m
Time Elapsed: t2-t1 = 0.91 s

v = d2 - d1 / t2 - t1
= 10m / 0.91s
= 10.99m/s
= 11m/s (approximately)

.:. The average velocity is approximately 11m/s.

20. Interval(m) 30-40m
Distance travelled: d2-d1= 10m
Time Elapsed: t2-t1= 0.87s (rounded to the nearest hundreth)

v=d2-d1/t2-t1
=10m/0.87s
=approximately 11.49m/s

.:. the average velocity is approximately 11.49m/s

21. Interval(m):30 to 40
Distance Traveled: d2-d1 = 10m
Time ElapsedL t1-t2 = 0.87s

v = d2 - d1 / t2 - t1
= 10m / 0.87s
= 11.5m/s
= 11m/s (approximately)