In Olympic Events, the 200m dash is an extremely fast race. One can compare the 'splits' of the time needed to complete the first 100m vs the second 100m. The second 100m of the 200m dash will be run faster than the 100m dash, for the simple reason that the runners have to start from rest in the latter. Treat the second 100m of the 100m dash as a constant velocity at their top speed. In the first 100m, the runner must start from rest and accelerate at a constant rate to reach their top speed (the same top speed as in the 2nd 100m). This top speed is reached very quickly, so make sure your model accounts for two different accelerations in the first 100m. The current record is Usain Bolt in 2009 with splits of 9.92s in the first 100m and 9.32s in the second 100m. a) Using data for the second split, determine Bolt's top speed, Utop.
In Olympic Events, the 200m dash is an extremely fast race. One can compare the 'splits' of the time needed to complete the first 100m vs the second 100m. The second 100m of the 200m dash will be run faster than the 100m dash, for the simple reason that the runners have to start from rest in the latter. Treat the second 100m of the 100m dash as a constant velocity at their top speed. In the first 100m, the runner must start from rest and accelerate at a constant rate to reach their top speed (the same top speed as in the 2nd 100m). This top speed is reached very quickly, so make sure your model accounts for two different accelerations in the first 100m. The current record is Usain Bolt in 2009 with splits of 9.92s in the first 100m and 9.32s in the second 100m. a) Using data for the second split, determine Bolt's top speed, Utop.
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Transcribed Image Text:In Olympic Events, the 200m dash is an extremely fast race. One can compare the 'splits'
of the time needed to complete the first 100m vs the second 100m. The second 100m of the
200m dash will be run faster than the 100m dash, for the simple reason that the runners
have to start from rest in the latter.
Treat the second 100m of the 100m dash as a constant velocity at their top speed. In the
first 100m, the runner must start from rest and accelerate at a constant rate to reach their
top speed (the same top speed as in the 2nd 100m). This top speed is reached very quickly,
so make sure your model accounts for two different accelerations in the first 100m.
The current record is Usain Bolt in 2009 with splits of 9.92s in the first 100m and 9.32s in
the second 100m.
a)
Using data for the second split, determine Bolt's top speed, Utop-
c)
In the first half of the race, Bolt accelerated with constant acceleration from rest to speed
Utop in time to and then ran at constant speed up for time top. Thus, 9.92s = ta+trop-
b)
In terms of a formula (not a number), what was Bolt's average velocity in
the constant acceleration portion? (Keep in mind that Bolt reaches top speed before
hitting 100m mark)
In terms of Utop, ta, and top, give expressions (not numbers!) for the distance
covered in the first half of the race.
d)
Using the fact that the distance and time for the first half of the race are 100
m and 9.92 s, determine numerical values for to and top-
Transcribed Image Text:c)
f)
On the diagram below make reasonably accurate sketches of Usain Bolt's
velocity and acceleration as functions of time according to the model we've worked out.
Be sure to indicate the scale for the velocity and acceleration graphs.
v (m/s)
What is the magnitude of the constant acceleration at the start of the race?
(₂S/W)D
10
5+
O
0
10+
5+
0
0
сл+
5
-10
5
+
10 15
10
20
15 20
t(s)
t(s)
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