The Starship Enterprise (variable acceleration problem) part II

In summary, the person is asking for help in understanding their mistake in a math problem they have been doing for the past two years. They provide the equations they have been using and someone points out an error in the last line of their calculations. After the correction, the person understands their mistake and hopes not to make it again.
  • #1
frankR
91
0
Okay what am I doing wrong? This is the way I've been doing math for the last two years. This is annoying me. Unless I've been doing everything wrong the last two years, I feel this is correct. I realize it's most likely wrong. Someone please explain to me what I am doing wrong and more important why.

F = -be^(-a*v) = m dv/dt, a and b are constants.

m [inte]vov e^(a*v) dv = -b [inte]to=0t dt

m/a e^(a(v - vo)) = -b*t

ln[e^(a(v - vo))] = ln[-abt/m]

a(v - vo) = ln[-abt/m]

v(t) = 1/a ln[-abt/m] + vo

dx/dt = v(t) = 1/a ln[-abt/m] + vo

[inte]xo=ox dx = [inte]to=ot1/a ln[-abt/m] + vodt

x(t) = t/a[ln(-a*b*t/m) + a*vo -1]
 
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  • #2
Originally posted by frankR
m [inte]vov e^(a*v) dv = -b [inte]to=0t dt

m/a e^(a(v - vo)) = -b*t

Your mistake is in the last line here. When you do the integral, you have to evaluate exp(av) at v and at v0 and subtract, to get:

exp(av)-exp(av0).

This does not equal:

exp(a(v-v0)),

which is what you have. Incidentally, this is the same basic mistake that I pointed out in "Part I" of this problem, except there you did it with the inverse function (natural log), when you used the invalid rule:

ln(a+b)=ln(a)+ln(b).
 
  • #3
m/a e^(a*v)|vov = -b*t

m/a(e^(a*v) - e^(a*vo) = -b*t

Okay now that makes sense.

Thanks.

Edit: Hopefully I won't make that mistake again.
 
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Related to The Starship Enterprise (variable acceleration problem) part II

1. What is the variable acceleration problem in relation to the Starship Enterprise?

The variable acceleration problem refers to the challenge of maintaining a constant acceleration for the Starship Enterprise as it travels through space. This is due to the fact that the ship's engines can only provide a limited amount of thrust, and the mass of the ship increases as it carries more fuel and crew members.

2. How does the variable acceleration problem affect the functionality of the Starship Enterprise?

The variable acceleration problem can have a significant impact on the functionality of the Starship Enterprise. It can make it difficult to accurately control the ship's speed and direction, and can also lead to issues with fuel consumption and navigation.

3. What solutions have been proposed to address the variable acceleration problem?

One solution that has been proposed is the use of a warp drive, which would allow the Starship Enterprise to travel at faster-than-light speeds and reduce the impact of variable acceleration. Another solution is to use a more advanced propulsion system that can provide higher levels of thrust and better control over acceleration.

4. How does the variable acceleration problem compare to other challenges faced by the Starship Enterprise?

The variable acceleration problem is just one of many challenges faced by the Starship Enterprise. Other challenges include managing the ship's power supply, dealing with potential malfunctions or technical failures, and navigating through various hazards in space such as asteroid fields or hostile alien ships.

5. Are there any real-world applications or implications of the variable acceleration problem?

While the variable acceleration problem may seem like a purely fictional challenge faced by the Starship Enterprise, it has real-world applications and implications in the field of space travel and exploration. As we continue to develop technologies that allow us to travel further and faster through space, the issue of variable acceleration will need to be addressed in order to ensure safe and efficient space travel.

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