Acceleration, velocity and position of a rocket

In summary, the conversation discusses finding the acceleration, velocity, and position of a rocket as a function of time. The equations for acceleration and velocity are provided, but there seems to be an issue with the units not working out properly. Potential causes for this issue include missing or incorrect conversion factors, the initial velocity and position not being consistent, and the direction of velocity and acceleration.
  • #1
Belginator
12
0
Hi everyone,

Quick question I may just not be thinking right here but I was trying to find the acceleration, velocity, and position of a rocket as a function of time. I started with acceleration:

[itex]a =\frac{T}{m-\dot{m}t} - g[/itex] where T is the Thrust, m is the initial mass, mdot is the mass flow rate, and g is gravity. This equation seems to work out with dimensional analysis and logically it seems to make sense, but maybe I'm wrong there. So from there I integrated wrt to time to get the velocity:

[itex]v = -\frac{T}{\dot{m}} ln(m-\dot{m}t) -gt + v_0 [/itex] Here is where the problem comes in, while I'm pretty sure I did my integration right, the units don't work out properly and velocity doesn't start out at 0 either, unless you set the [itex] v_0 [/itex] term to some value. Finally I tried to get position by integrating v:

[itex]s = \frac{T}{\dot{m}^2} ((m-\dot{m}t)ln(m-\dot{m}t) - (m-\dot{m}t)) - 0.5gt^2 + v_0t + s_0 [/itex] Again the units don't work out properly.

I'm just considering where the rocket goes vertical for now, no horizontal components.

What am I not seeing here? This should be fairly straight forward. Thanks in advance for any help.
 
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  • #2
Hi Belginator! :smile:
Belginator said:
[itex]v = -\frac{T}{\dot{m}} ln(m-\dot{m}t) -gt + v_0 [/itex] Here is where the problem comes in, while I'm pretty sure I did my integration right, the units don't work out properly and velocity doesn't start out at 0 either, unless you set the [itex] v_0 [/itex] term to some value.

No, the units are fine.

ln has no units (like sin) …

your ln(m-m't) + vo is really ln((m-m't)/(mo)) for some constant mo :wink:
 
  • #3


Hi there,

I'm not an expert in physics, but I'll try my best to help you out. From what I can see, your equations seem to be correct. However, the issue with the units not working out properly could be due to some missing or incorrect conversion factors. For example, make sure that all the units for mass, time, and velocity are consistent throughout your equations.

Also, for the initial velocity (v0) to be 0, the initial position (s0) also has to be 0. So if you're assuming that the rocket starts at the ground, then v0 and s0 should both be 0.

Another thing to consider is the direction of your velocity and acceleration. Are you assuming that they are both in the same direction? If not, then that could also affect the units and values of your equations.

Overall, it seems like your equations are on the right track, but there may be some minor errors or missing factors that are causing the units to not work out properly. I would suggest double-checking all the units and making sure they are consistent, and also considering the direction of the velocity and acceleration.

Hope that helps! Let me know if you have any other questions.
 

1. What is the difference between acceleration, velocity, and position of a rocket?

Acceleration is the rate of change of velocity, or how quickly the velocity of a rocket is changing. Velocity is the rate of change of position, or how quickly the position of a rocket is changing. Position is the location of the rocket in space at a given time.

2. How do you calculate the acceleration of a rocket?

The acceleration of a rocket can be calculated by dividing the change in velocity by the change in time. This can be represented by the formula a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

3. How does thrust affect the acceleration of a rocket?

Thrust is the force that propels a rocket forward. The greater the thrust, the greater the acceleration of the rocket will be. This is because thrust is one of the factors that contribute to the overall force (along with mass and gravity) that determines the acceleration of a rocket.

4. Can a rocket have a negative velocity or acceleration?

Yes, a rocket can have a negative velocity or acceleration. This simply means that the rocket is moving in the opposite direction of its initial velocity or is slowing down in its motion. Negative acceleration can also be referred to as deceleration.

5. How do you calculate the position of a rocket at a given time?

The position of a rocket at a given time can be calculated by multiplying the average velocity by the time interval and adding it to the initial position. This can be represented by the formula x = vavg * t + xi, where x is the position, vavg is the average velocity, t is time, and xi is the initial position.

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