A world class sprinter accelerates from rest to his maximum speed in 4.00s. He then maintains that speed for the remainder of a 100.m race. He is able to finish the race in 9.10s.
a) What is the average acceleration for the first 4.00s?
b) What is his average acceleration for the final 5.10s?
c) What is his average acceleration for the entire race?
I worked backwards and began with c.
c) x = v(t) + 1/2a(t^2)
100m = (0 * 9.10s) + 1/2a(9.10s)^2
a=2.42m/s^2 for the entire race.
b) avg acceleration is 0 m/s^2; he maintained his velocity for the second 5.10 seconds.
a) A is where I think the problem breaks down or I'm not understanding it correctly.
The average velocity is 11m/s (100m/9.10s), and using this we can find the final velocity.
avg v = 1/2 (v-initial+v-final)
11 m/s= 1/2 (0m/s+vf)
vf=22m/s
Then, to find the acceleration for this part,
vf=vo+at
22m/s=0m/s+a*4.0s
a=5.5m/s^2.
This acceleration and final velocity would disobey the 100m overall guideline. He travels 44m accelerating to 22m/s in 4.0s, then runs at 22m/s for 5.10s. Overall, he has traveled 156m, traveling 112m in the final 5.10s stretch. Could someone please find the flaw in my logic or the flaw in the problem?
Thank you very much!
a) What is the average acceleration for the first 4.00s?
b) What is his average acceleration for the final 5.10s?
c) What is his average acceleration for the entire race?
I worked backwards and began with c.
c) x = v(t) + 1/2a(t^2)
100m = (0 * 9.10s) + 1/2a(9.10s)^2
a=2.42m/s^2 for the entire race.
b) avg acceleration is 0 m/s^2; he maintained his velocity for the second 5.10 seconds.
a) A is where I think the problem breaks down or I'm not understanding it correctly.
The average velocity is 11m/s (100m/9.10s), and using this we can find the final velocity.
avg v = 1/2 (v-initial+v-final)
11 m/s= 1/2 (0m/s+vf)
vf=22m/s
Then, to find the acceleration for this part,
vf=vo+at
22m/s=0m/s+a*4.0s
a=5.5m/s^2.
This acceleration and final velocity would disobey the 100m overall guideline. He travels 44m accelerating to 22m/s in 4.0s, then runs at 22m/s for 5.10s. Overall, he has traveled 156m, traveling 112m in the final 5.10s stretch. Could someone please find the flaw in my logic or the flaw in the problem?
Thank you very much!
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Hi John, where your analysis falls down is when you assume that:
avg v = 1/2 (v-initial + v-final)
This would be true if the acceleration was constant throughout the race, however the acceleration is limited to the first 4 seconds. Indeed the average velocity is 11m/s, and clearly the final velocity will be greater than 11m/s, since the first 4 seconds of the race were run mostly at a velocity of less than 11m/s.
avg v = 1/2 (v-initial + v-final)
This would be true if the acceleration was constant throughout the race, however the acceleration is limited to the first 4 seconds. Indeed the average velocity is 11m/s, and clearly the final velocity will be greater than 11m/s, since the first 4 seconds of the race were run mostly at a velocity of less than 11m/s.