Can a Runner Accelerate to Finish a 10,000 Meter Race in Time?

[jehan4141]

Please interpret this problem as you will. My professor and I seem to have different interpretations of this problem.

A runner hopes to complete the 10, 000 meter run in less than 30 minutes. After exactly 27.0 minutes, there are still 1100 meters to go. For how many seconds must then the runner accelerate at 0.20 m/s² to achieve the desired time?

The Attempt at a Solution

My interpretation was that he can run the entire 10,000 meters in LESS than 30 minutes. So this is what I did:


1. I found that starting from rest, he can run the first 8900 meters in 27 minutes.

10000-1100 = 8900 m
t = 27(60) = 1620 seconds

Thus the average velocity is v = x/t = 8900/1620
v=5.49382716 m/s

2. I know that when this velocity is reached, he starts to accelerate at a = 0.2 m/s². So I call it V_i.

Starting from V_i = 5.49 m/s, he has 1100 meters left to run.
Using the equation x = x_o + V_it + 0.5at² I get
1100 = 5.49t + 0.5(0.2)t²

Cleaned up you get
0.1t² + 5.49t - 1100 = 0
Solve. T = 80.94928247

Is my answer correct? My teacher's answer is different than mine. Did I misinterpret the problem somewhere? How is your interpretation? Thank you!

 

[hotvette]

Your approach assumes the acceleration remains until the race is finished, so the runner's total time is ~28:20. I suspect the intent of the problem is to find out how long the runner needs to accelerate, then coast at the final velocity, to finish the race in exactly 30 minutes. I know the problem statement say's 'under', but how much under isn't stated, so I think the problem could have been worded better.

 

[jehan4141]

I believe you are correct. Her email said that. I would never have interpreted the problem that way :( let's hope the quiz isn't like that! Thank you so much!

 

[hotvette]

One thing you can do in a situation like this is state that the probem is not clear and why, then list the assummptions you choose to use (because the wording isn't clear) and solve the problem. You might get partial credit if you solve a different problem than what was intended but make a good logical case.

 

[rwisz]

I would say that both interpretations are valid and can lead to different solutions. However, I would also suggest that it is important to clarify the problem with your professor to ensure that you are both on the same page. In my interpretation, the runner's goal is to complete the entire 10,000 meter run in less than 30 minutes, not just the remaining 1100 meters. Therefore, the runner must accelerate at 0.20 m/s2 for the entire 10,000 meters in order to achieve the desired time. This would result in a different solution than your approach. It is possible that your professor may have a different interpretation of the problem or may have made a mistake in their solution. It is always important to communicate and clarify any discrepancies in problem interpretation to ensure accurate solutions.