Constant acceleration except time?

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Homework Help Overview

The discussion revolves around a problem involving two runners accelerating at constant rates, where the goal is to determine the ratio of their accelerations based on their times to finish a race. The original poster expresses confusion regarding the use of time ratios and the calculations leading to different results compared to an answer key.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the relationship between the times taken by the runners and their respective accelerations. Questions arise about the interpretation of the time ratio and the reasoning behind using specific calculations, such as the inverse of the time ratio squared.

Discussion Status

The discussion includes various interpretations of the problem and attempts to clarify the relationships between the variables involved. Some participants provide insights into the reasoning behind the calculations, while others express uncertainty about the assumptions made in the problem setup.

Contextual Notes

There is mention of the original poster's confusion regarding the time ratio and how it applies to the runners' accelerations. Additionally, the discussion reflects on the importance of understanding the scaling of variables in physics equations.

Lori

Homework Statement


upload_2017-12-9_18-32-52.png


Homework Equations



d = vit + 1/2at^2

The Attempt at a Solution



Hey, so what i did was different from the answer key above. Instead of (4/5)^2 i did 1/ (4/5^2) so i got 25/16 as the answer. I'm not sure why tb/ta = 4/5 since 4/5 the time is referring to runner b's time? Why is it combined here?[/B]
 

Attachments

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Runner B is gets to the finish line first. You are asked for the ratio of runner A's acceleration to that of runner B. Which one accelerated faster?
 
Why did you use 1/(4/5)^2?
 
jbriggs444 said:
Runner B is gets to the finish line first. You are asked for the ratio of runner A's acceleration to that of runner B. Which one accelerated faster?
Runner b because both runners ran at constant acceleration
 
Lori said:
Runner b because both runners ran at constant acceleration
nvmd, i was able to get the answer. I had to solve for a for both runners and plug in time, and then put them in ratio
 
The slow guy took ##T## time. The better one did the same distance ##x## in ##0.8T##. You correctly observed that in this instance, ##x=\frac{1}{2}at^2##. We have two equivalent ##x##'s since they ran the same distance. Let's carefully label our accelerations, ##a_1## for the slow guy and ##a_2## for the fast one. Now

$$\frac{1}{2}a_1 T^2=\frac{1}{2} a_2 (0.8T)^2$$

Which easily simplifies to ##a_1=0.64a_2##. Since we want ##\frac{a_1}{a_2}##, we can just rearrange and find that ##\frac{a_1}{a_2}=0.64=16/25##.

When questions ask for the ratio of the same variable in different conditions, it's very useful to think about how that variable scales in its appropriate equation. For example, since time squared runs proportional to acceleration, this problem becomes immediate. I knew the answer was either ##16/25## or ##25/16## but I used logic to sort out which it would be by considering which person's acceleration was greater. So you need to work on thinking about your variables logically. The biggest piece of advice I can give you for physics is that you should be actively applying "physics thinking" to the algebra part. What I mean is that you can't expect to just set up equations using physics and then only use algebra. This works fine with basic problems, but as you get more advanced you will need to be following your algebra with much more than just a mathematical eye. This will motivate more complicated solutions, especially when you're struggling to find useful substitutions.
 

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