## Background

One definition of velocity is *the speed of something in a given direction (*illustrated in the picture below). Velocity is measured as a change in position over time, such as 25 miles per hour, or 5 feet in a second. If velocity is constant, it’s the amount of time that it takes to travel the distance.

Isaac Newton defined an important law for velocity in the 17th century stating that an object at rest (no velocity) stays at rest unless a force is applied. Velocity and force are linked together in Newton’s first law of motion.

The first law also states that an object in motion will stay in motion with the same speed and in the same direction (i.e. velocity) unless a force is applied. This means that an object can change its position, i.e. it is moving, even if there is no force. This led to Newton’s second law, explaining a change in velocity over time, which is acceleration.

Velocity is a change in position over time. Acceleration is a change in velocity over time.

See also: Acceleration

## Newton’s First Law of Motion

The first law of motion states that a body will remain at rest, or continue at a constant velocity, unless a force is applied. Essentially, velocity is always constant. At rest, velocity remains zero. While in motion, velocity remains the same until a force is applied.

At rest, a particle or body’s acceleration (a) is zero and velocity (v) is zero. The figure below describes a particle that has a particle core of one or more wave centers, a standing wave structure that extends to the particle’s radius, and spherical, longitudinal traveling waves beyond this radius. Standing waves are generated by in-waves that are reflected to become out-waves. At rest, the wavelength of the standing waves (λ_{lead}) matches the wavelength of the in-waves (λ_{l}). There is no wavelength/frequency difference between the particle and its surrounding environment. The particle is at rest and will remain at rest.

** Note: **The traveling wave is a spherical, longitudinal wave. The figure above illustrates a simple sine wave as this wave due to the difficulties describing a three-dimensional wave in a two-dimensional image. But it’s important to note that it is a not the transverse wave associated with photon energy (described separately in the Photons section).

A particle in motion has a velocity greater than zero. With no acceleration (a=0), velocity remains constant according to Newton’s first law of motion. To an observer, the wavelength on the leading edge (λ_{lead}) of the particle is compressed, in the direction of motion, relative to the longitudinal, traveling in-waves (λ_{l}). There is a wavelength or frequency difference with the external environment, which was shown to follow Doppler equations. This frequency difference is the basis of the calculation for velocity, as it will be shown mathematically. It is also the reason particles (and thus objects that are built upon particles) experience time dilation and length contraction in the direction of motion.

The figure below illustrates a particle in motion with no acceleration. Wave amplitude is constant and equal on all sides of the particle. The particle will maintain its standing wave frequency on both the leading and lagging edges of the standing wave structure, although it is different than its external environment. Wavelength on the leading edge is less than the wavelength of the in-waves (λ_{lead} < λ_{l}) and will remain constant. The smaller the leading edge wavelength, the greater the velocity. If the particle core reaches the edge of its standing wave radius, the leading edge wavelength is near zero, and its velocity is nearly the speed of light.

### Doppler and the Velocity Equation

Velocity results in a difference in wavelength. The Doppler effect is apparent in the image above of a moving particle and is the basis of how the Velocity Equation is derived. The ratio of the fundamental wavelength and the wavelength of the leading edge of the particle is defined as:

Now, velocity (v) is introduced in wave constant terms. Since the speed of light (c) and the fundamental wavelength (λ_{l}) are both constants, velocity is proportional to the leading edge wavelength (λ_{lead}).

To solve for velocity, the next step was to solve for the leading edge wavelength. The leading edge wavelength is derived from acceleration (Acceleration Wavelength at Time equation), which itself is derived from the Force Equation because acceleration and force are related. When substituting the leading edge wavelength equation from acceleration, velocity can be finally solved. The detailed derivation is found in Section 6 of the *Forces* paper.

**Velocity Equation**

The Velocity Equation can be used to model any group of particles (Q) at distance (r) at time (t), assuming constant acceleration. Also, note that the simplified version of the Velocity Equation assumes a particle begins at rest.

Gravity is a form of constant acceleration, at least when measured close to the surface of a planet. For example, calculations for gravity on Earth are normally calculated at 9.81 m/s^{2} – constant acceleration. Thus, velocity was cross-checked with velocities of falling bodies due to gravity to validate the equation. However, the equation requires a modification for the amplitude factor for gravity, as gravity is a slight loss of wave amplitude. The equation is modified to have this factor. Q is the particle count for large bodies and α_{Gp} is the amplitude difference for nucleons; both are described in the section on Gravity. μ is the proton-to-electron mass ratio.

**Velocity Equation for Gravity**

A benefit of deriving velocity based on wavelength is that relativity is naturally built into the equation. Velocity can never be greater than the speed of light. It’s true in the equation, but it also has an explanation. The particle’s leading edge wavelength cannot be less than zero. This was also proven in the velocity calculations when using relativistic speeds (as a result of large accelerations over a long period of time). The maximum speed is the speed of light in these calculations.

## Proof

The velocities of falling bodies on various planets at various times were calculated accurately in the calculations as proof of the Velocity Equation for Gravity. Velocity can be modeled based on wave constants and a difference in wavelength. An example is provided to illustrate the calculation and proof.

Earth – Velocity of Falling Body after 50 seconds from rest: Velocity is based on time, so the first calculation is based on a falling object on Earth, which starts at rest, and has a calculated velocity after 50 seconds (t). Using the Velocity Equation for Gravity above, the number of nucleon particles for Earth was calculated is used as Q_{group} (refer to the Gravity section for calculation of nucleons). The radius of the Earth, r_{group}, is 6,375,223 meters. The proton to electron mass ratio is μ = 1836.152676.

t = 50 s

r_{ earth} = 6,375,223 m

Q_{earth} = 3.570 x 10^{51}

**Calculated Value: **490.33 m/s

**Difference:** 0.000%

* Note: *A summary of various velocity calculations is found on this site; more detailed calculations with instructions to reproduce these calculations is found in the

*Forces*paper.