Shouldn't these equations produce the same result?

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In summary, a pilot starting from rest can reach Mach 4 in 33.7 seconds without graying out and the plane would travel 22,392 meters during this period of acceleration.
  • #1
Breadsticks
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Homework Statement


If a pilot accelerates at more than 4g, he begins to “gray out” but doesn’t completely lose consciousness. (a) Assuming constant acceleration, what is the shortest time that a jet pilot starting from rest can take to reach Mach 4 (four times the speed of sound) without graying out? (b) How far would the plane travel during this period of acceleration? (Use 331 m s for the speed of sound in cold air.)

Homework Equations


2aΔx=V2-V02
Δx=V0t+(1/2)at2

The Attempt at a Solution


I was reviewing my work for the chapter and came across a problem with part b. I used 2aΔx=V2-V02 instead of Δx=V0t+(1/2)at2 like I did the first time. The time it takes is 33.7 seconds, and initial velocity is zero with final velocity being 1324 m/s. The acceleration is 39.24 m/s2. Using the second equation, I get the right answer of 22392 m. But using the first equation, I get 2087 m. Why is this? If there is a final velocity and an initial velocity, and acceleration is the same with both, wouldn't it have to take the same time?
 
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  • #2
Breadsticks said:

Homework Statement


If a pilot accelerates at more than 4g, he begins to “gray out” but doesn’t completely lose consciousness. (a) Assuming constant acceleration, what is the shortest time that a jet pilot starting from rest can take to reach Mach 4 (four times the speed of sound) without graying out? (b) How far would the plane travel during this period of acceleration? (Use 331 m s for the speed of sound in cold air.)

Homework Equations


2aΔx=V2-V02
Δx=V0t+(1/2)at2

The Attempt at a Solution


I was reviewing my work for the chapter and came across a problem with part b. I used 2aΔx=V2-V02 instead of Δx=V0t+(1/2)at2 like I did the first time. The time it takes is 33.7 seconds, and initial velocity is zero with final velocity being 1324 m/s. The acceleration is 39.24 m/s2. Using the second equation, I get the right answer of 22392 m. But using the first equation, I get 2087 m. Why is this? If there is a final velocity and an initial velocity, and acceleration is the same with both, wouldn't it have to take the same time?
You certainly miscalculated something. Both method gives the same result.
 

1. Why do the equations produce different results?

The equations may produce different results due to a number of reasons. It could be that the equations are solving for different variables, have different assumptions or boundary conditions, or are using different methods of approximation. It is important to carefully examine and compare the equations to identify the source of the discrepancy.

2. Can one equation be considered more accurate than the other?

It is possible that one equation may be more accurate than the other, but this cannot be determined without further analysis. The accuracy of an equation depends on its underlying assumptions and how well it reflects the real-world phenomenon it is trying to model. Both equations should be evaluated and validated against experimental data to determine their accuracy.

3. How can I decide which equation to use?

The appropriate equation to use depends on the specific problem at hand and the desired level of accuracy. It is important to carefully examine the assumptions and limitations of both equations and choose the one that best fits the problem and provides the necessary level of accuracy. In some cases, a combination of equations may be necessary to accurately model a complex system.

4. Are there any other factors that could affect the results of the equations?

Yes, there could be other factors that affect the results of the equations. These could include measurement errors, human error in inputting data, or external factors that were not taken into account in the equations. It is important to carefully assess all possible sources of error and try to minimize their impact on the results.

5. Can I modify the equations to produce the same result?

It is possible to modify the equations to produce the same result, but this should only be done after careful consideration and validation. Changing the equations could alter their accuracy or applicability to the problem. It is important to understand the underlying principles and assumptions of the equations before making any modifications.

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