Determining Maximum Velocity of an object traveling horizontally I'm in the process of working on a physics related game.  I'm looking to find the maximum velocity of an object given it's mass and the force acting on it when it is traveling horizontally.  I believe there must be a method of calculating this but I'm unaware of it.  Is there a formula for this scenario?  I'm unaware if this is the same calculation as terminal velocity but I don't believe it is.  Thanks for any help!
 A: Suitable for game physics and BoTE calculations:


*

*Assume a functional form for the frictional resistances (all the apply from rolling, sliding and fluid (wind or water)), and solve for the total resistance equal to the driving force.

*If that does not limit the speed to a reasonable velocity and this even takes place on a planet, compute the orbital velocity at that elevation. Above that speed a downward force will have to be applied to maintain local horizontalness for the motion...
Toward (1):


*

*rolling and sliding friction tend to be independent of speed, except that heat dissipation may cause secondary effects. 

*Wind resistance is generally proportional to $v^2$ except in the neighborhood of the speed of sound. 

*Water resistance for surface vessels is complicated with several parts proportional to square (viscous) and cubic (wave making) terms at least.

A: Assume the object is moving on a frictionless surface in the absence of a gravitational field with a certain velocity or it is at rest. Calculate the kinetic energy of this object as a result of its uniform motion or rest. The formula for kinetic energy is:$K.E \ =\  \Large \frac{1}{2} \large mv^2$
Applying a force for a certain distance on thsi object imparts energy to the body, which immediately manifests as a change in velocity and a resultant change in its total kinetic energy. 
Then the energy imparted to the object will be:$E\ =\ \large F\times d$Here 'F' is the force applied, and 'd' is the displacement over which the force has been applied. After the effect of the force wears out, a uniform velocity is attained by the object which can be calculated by combining the above two equations:
$\Large v\ = \ \sqrt{\frac {2(K.E\ +\ E)}{m}}$
I must tell you that I am 15 years old and this is simply an idea I've provided for your perusal. This idea is given in the context of classical mechanics. 
