# 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!

• I think before calculating the maximum velocity, you have to identify the physical mechanism that would make there be a maximum velocity in the first place. – David Z Jan 31 '11 at 2:54

## 2 Answers

Suitable for game physics and BoTE calculations:

1. 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.

2. 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.

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.