## Background

Acceleration is the rate of change of velocity with respect to time. For example, push on the gas pedal to accelerate a car, and it changes velocity (speed in a given direction). Push on the brake, and it decelerates and will decrease velocity. If the car hits another object and decelerates, the force of the impact is based on the acceleration or deceleration, not the velocity of the car.

Isaac Newton’s second law of motion states that the sum of all forces (F) is equal to mass (m) multiplied by acceleration (a), or F=ma. Thus, acceleration and force are intimately linked with this law.

See also: Velocity

## Newton’s Second Law of Motion

In the first law of motion, when described in wave terms, wavelength may differ but wave amplitude is constant.

In the second law, wave amplitude is not constant and is the reason for force and acceleration. Particles move to minimize amplitude, one of the laws of energy wave theory. The first figure below describes a particle, initially at rest (v_{i}=0), now accelerated (a>0). A particle will move in the direction of minimal amplitude, thus the leading edge in the acceleration and velocity equations always refer to the direction in motion where wave amplitude is less than the amplitude in any other direction surrounding the particle. Similarly, the amplitude in the direction of motion is described using the same notation (A_{lead}). This amplitude difference leads to a force on the object and it is accelerated. The particle core will move from its resting position to a new frequency.

**Note: **See Velocity (Newton’s First Law of Motion) for a more detailed legend and description of the components in the image above.

The next figure (below) describes the change in position of the particle core due to acceleration, which is caused by amplitude difference. Acceleration is the change in the position of the particle core, affecting wavelength and frequency. A smaller acceleration value moves the particle core slower towards its edge, and a larger acceleration value moves the particle core faster towards its edge. This requires a measurement of time to define *slower* or *faster*. Time is based on wavelength cycles (which is frequency), thus acceleration is the movement of the particle core towards the edge of the radius based on the number of wavelength cycles. This is seen in the Acceleration Equation.

Newton’s first law of motion is based upon wavelength. The second law is based upon wave amplitude. And for the derivation and proof of these laws under energy wave theory, the starting point is acceleration, using the Force Equation.

## Proof

Proof of the energy wave explanation of acceleration is rooted in the derivation of the Force Equation itself, as acceleration and mass are proportional to force. This is illustrated in a summary of the derivation below and its relation to Newton’s law and Coulomb’s law. The first proof is based on a derivation of force equations; the second proof is based on calculations that match existing data and experimental evidence. The Acceleration Equation is used in gravity equations to calculate acceleration due to gravity, and shown to be an accurate method of calculating surface gravity.

### Newton, Coulomb and the Force Equation

When solving the force for Newton’s law, Coulomb’s law and using the Force Equation for two single electrons, all forces are found to be equal in both the calculations and the derivation. Each of the constants and variables for Newton’s law and Coulomb’s law have equivalents in energy wave theory. They are found in the Constants section.

There is one force. The summary of these three force equations appears as the following:

The complete derivation, breaking each of these equations into their wave components and illustrating that they are equal is found in the *Forces *paper. Due to its length, it is not repeated here. What is important in the derivation steps is that the leading edge wavelength changes based on amplitude and time. The ratio of leading edge wavelength and the fundamental wavelength is:

**Acceleration Wavelength at Time (t)**

Also in the derivation, acceleration is found to be a component of the Force Equation. It is derived in the equation to be:

**Acceleration Equation**

To calculate the acceleration for gravity, the amplitude loss needs to be considered. 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.

**Acceleration Equation for Gravity**

### Example Calculation

The surface gravities of 11 planets were calculated accurately in the calculations as proof of the Acceleration Equation for Gravity. Acceleration can be modeled based on wave constants and a difference in amplitude. An example is provided here to illustrate the calculation and proof.

Earth Surface Gravity: The Acceleration Equation for Gravity is used to calculate the surface gravity for Earth. The number of nucleon particles for Earth was calculated and 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.

r_{ earth} = 6,375,223 m

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

**Calculated Value: **9.807 m/s^{2}

**Difference:** 0.000%

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

*Forces*paper.