# Power and Acceleration

1. Dec 30, 2007

### Mutos

[SOLVED] Power and Acceleration

Hi all,

I'm posting here because I see an apparent paradox between what intuition and equations tell me. I'm sure it's a question of referential or something like that, but I just can't see it clearly...

So it's all about power and acceleration. Suppose the following situation : consider a spaceship under constant acceleration. Let's say it's a fictionary reactionless propulsion and not bother about fuel depletion, efficiency or other topics : ship mass stays constant, all energy is used for propulsion, there is no friction at all and we do not reach relativistic speeds.

Intuitively, you will say that this ship would use for its propulsion a constant power output. Thrust is the same at all time, forces and the physical mechanism that produce them are the same, so power output should be the same. Intuitively, a ship with a given power unit should be able to sustain constant acceleration infinitely, given we take out the fuel, efficiency and other problems.

But equations say that power depends on time as speed must be considered to compute the link between power and acceleration. They say P=m.a^2.t and so says the unit check : W=kg.m.s^-3, which is consistent with the formula.

It's been 15 years since I've not taken to this kind of physics problems, now I tangle only with IT problems, and so I fear I'm a little rusty by now. I'm sure the answer is simple, but I've lost something essential in my reasoning... Thanks for any hint to find it back ^-^

2. Dec 30, 2007

### Mutos

Hi all,

I'm just replying to myself as I've found a thread talking about that. I missed it in my initial search so I'll link to it and see if it allows me to better understand. Already the first page begins talking about frames of reference so it must be the right directino to check...

It's just a question of frame of reference and the keyword in this cas is measured energy. That is, if you measure the energy of the same object relative to different reference frames, you'll have different answers...

Last edited: Dec 30, 2007
3. Dec 30, 2007

### Cyrus

Power: $$H.P.=\frac{FV}{550}=\frac{F}{550}\frac{dx}{dt}$$

Acceleration: $$a=\frac{d^2x}{dt^2}$$

I dont see where constant power output is coming from? If your engines put out a constant force, then the velocity increases, and so does the power.

Last edited: Dec 30, 2007
4. Dec 30, 2007

### Mutos

Hi Cyrus, hi all,

Thanks Cyrus for answer. In fact is's all about perception vs measurement, the equations have nothing to do with it, I know they're right and my perception is wrong. The problem is "Why ?" and the answer has to do with frames and the way we think about power and energy.

In my answer to the relevant thread I try to explain that in further details :
https://www.physicsforums.com/showpost.php?p=1555944&postcount=75

I just don't know how to close this post to keep it distracting the attention of forumers from the relevant one where the topic has been discussed in details. In fact I should never have posted in the first place, but I searched badly and didn't find the already existing post...

Last edited: Dec 30, 2007
5. Dec 30, 2007

### Cyrus

6. Dec 31, 2007

### animalcroc

Your formula is correct. Power is given by the change in kinetic energy over time, i.e. the derivative of KE with respect to time. Since KE=(1/2)m*v^2, where v is a function of time, d(KE)/dt=m*v*a=a*m*(a*t)=m*a^2*t
Let's consider a constant force acting upon a body, in this case a falling apple. The apple's speed increases linearly with time. So, the equation for power (force*velocity) is linear in time.

Last edited: Dec 31, 2007
7. Dec 31, 2007

### animalcroc

I edited my post.

8. Dec 31, 2007

### animalcroc

Now for the perception part. Power increases with time because the apple moves faster. Power has to do with the work put in over a time interval. The faster something moves, the more work (force*DISTANCE) can be put in over a given time interval.