# Formula for getting energy required to accelerate to a certain speed?

I am curious how many newtons it takes to accelerate an object with a given coefficient of drag, reference area, weight, and air pressure? I know this may sound like a simple equation but I have no idea where to find this formula.

Thanks.

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do you want to accelerate your object in a certain time frame? If not, it is enough to just apply more force than the drag force for which the formula is given by Wikipedia. – luksen Sep 1 '11 at 16:24
$\sum F = ma$ ? To calculate without disregarding wind-drag can be complicated... – Nic Sep 1 '11 at 16:29
Complicated, yeah, but I want to compare this energy at two different altitudes / pressures – Kyle Hotchkiss Sep 1 '11 at 21:31
Do you want energy, or force? This question cannot be answered as is. – Ron Maimon Sep 6 '11 at 2:37

Use Stokes' equation. Since you're referring to drag, pressure and area, I assume that you're referring to motion of objects in fluids.

So this question would come under fluid mechanics.

Of course if you're trying to find a relationship between acceleration and force; that is, you want to know how much force it will take for you to cause the object to move with a certain acceleration in a fluid medium (since that's where you're getting drag), and since you referred to air pressure, I'm guessing that your 'fluid medium' is air.

Well, the effect of reference area is that it causes the drag to vary: generally you're going to get more drag with more reference area, assuming you're using the same shape (i.e. spheres of different sizes).

To be honest, you really need to be specific about what air pressure has to do with anything here. I have no idea what air pressure has to do with this, unless you’re referring to spinning ping pong balls, in which you have air pressure causing a change in the direction of motion (velocity) of the ping pong ball which spins in air.

If you want a more general equation, you might be looking for the Navier-Stokes equations.

Note that the effect of having drag is that it causes the net force acting on the ‘object’ that you’re trying to accelerate to change. We’ll have to use Newton’s second law (F=ma) to calculate the acceleration once you know the net force acting on the object.

http://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations http://en.wikipedia.org/wiki/Stokes'law (physics">http://en.wikipedia.org/wiki/Drag_(physics)

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Of course you can find tonnes of information of motion of fluids on the internet. just google terms like 'drag coefficient' – raindrop Sep 3 '12 at 1:46

Acceleration is rate of change of speed - so it all depends on how long you want it to take.

I can lean on the front of a railway locomotive and with a tiny force start it moving very-very slowly (assuming I can overcome static friction on the wheels). But if I want it to go from 0-60 in under 3seconds I am going to need a rather large engine

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