Motion Related Equations
For the sake of sanity, the use of calculus is kept to a strict minimum.
 

New Velocity

VNew = VOld + AT

    This equation is used to get a new velocity after a known old velocity plus a known period of known acceleration.  VNew is the new velocity, while VOld is the old and known velocity.  The variable A is for acceleration, and T is for time.  Please be sure that A, VOld , and VNew are in the same units as each other (i.e. meters / second).  For slowing down (deceleration), just use a negative value for A.
 
 

Distance Traveled with Linear Acceleration / Deceleration

XNew - XOld = 1/2 (VNew + VOld ) T

    This equation is used to get the distance traveled when the old and new velocities and time are known. VNew is the new velocity, while VOld is the old and known velocity.  The variable A is for acceleration, and T is for time.  Please be sure that VOldand VNew are in the same units as each other (i.e. meters / second).  Likewise, be sure that XNew and XOld are in the same distance units as that used in VOld and VNew.
 
 

Another Equation for
Distance Traveled with Linear Acceleration / Deceleration
(Acceleration Is Known.)

XNew - XOld = VOldT + 1/2 AT2

    This equation is used to get the distance traveled when the old velocity, time, and acceleration are known.  VNew is the new velocity, while VOld is the old and known velocity.  The variable A is for acceleration, and T is for time.  Please be sure that VOld , VNew , and A are in the same units as each other (i.e. meters / second).  Likewise, be sure that XNew and XOld are in the same distance units as that used in VOldand VNew. For deceleration, use a negative value for A.
 
 

New Velocity Based on Acceleration / Deceleration
and Distance Traveled

VNew2 = VOld2 + 2A ( XNew - XOld )

    This equation is used to get a new velocity after a known old velocity plus a known period of known acceleration.  VNew is the new velocity, while VOld is the old and known velocity.  The variable A is for acceleration, and T is for time.  Please be sure that A, VOld , and VNew are in the same units as each other (i.e. meters / second).  For deceleration, just use a negative value for A.
 
 

Distance Traveled with Varying Speed Over Time

XNew - XOld = VAverage T

OR

XNewAAAA
  V  dT
XOldAAAA

CAUTION:  CALCULUS IS PRESENT HERE!  Guard thy sanity!

    This equation is used to get the distance traveled over a period of time when the velocity varies. is the velocity function of time.  Please be sure that XOld , and XNew are in the same units as each other (i.e. meters / second).
 
 

Splitting Up X, Y, and possibly Z Components of An Angled Path

X = L  COS (q)
and
Y = L  SIN (q)
and possibly
Z = L  SIN (qX-Z Plane)

    These equations is used to get the X and Y components of an angled line whose length is L.  The third equation is required only when working in 3-D.  The Z part is from the X-Z plane.
 
 

Distance Between Two Points

D = ( X2 + Y2+ Z2 )1/2

    This is the standard 3-D distance formula.  When working in 2-D, just omit the Z part or just give it a value of 0.
 
 

Basic Force Equation

F = MA

    This equation is used to calculate force on a given mass of an object and its acceleration (or deceleration by using a negative value).  Also, a negative value can mean acceleration in the OPPOSITE direction.  F is the net force in newtons or 1 Kg * M/s2.  That means if a mass of 1 kilogram (which is 2.204623 lb when at sea level on Earth) is decelerated by one meter per second (acceleration = -1),  it would take a force of 1 newton to stop it.  For British use, F is in the units of pounds and M is in units of slugs, which is a British unit for mass, and A is in units of ft/s2.  Please note that WEIGHT is also a force, but is composed of MASS x ACCELERATION.  In place of A, use 9.803 if in m/s2 or use 32.162 ft/s2, which is the acceleration caused by Earth's gravity at sea level. a a
 
 

Linear G-Force

F = (( VOld - VNew ) / T ) / G

    This equation is used to calculate linear G-force.  VNew is the new velocity, while VOld is the old and known velocity.  The variable G is for acceleration, and T is for time.  Please be sure that G, VOld , and VNew are in the same units as each other (i.e. meters / second).  For deceleration, just use a negative value for G.
 
 

Centrifugal G-Force

F = ( V2 / R ) / G

    This equation is used to calculate centrifugal G-force.  V is the velocity, while R is the radius.  The variable G is for gravity.  Please be sure that G and V are in the same units as each other (i.e. meters / second).
 
 

Centrifugal G-Force Using RPM's

F = ( (2pR(N/60))2 / R ) / G

    This equation is used to calculate centrifugal G-force when the number of revolutions per period of time and the radius are known.. N is the number of circles (Fractionalcircles are included as a fraction.) made within a unit of time (i.e. second), while R is the radius.  The variable G is for gravity.  Please be sure that G and R are in the same distance units as each other (i.e. meters).  Whatever unit of time is used, make sure that it is reflected in both the number of circles made and in the time unit used in accelerationdue to gravity.  For your information, Earth's gravity results in a G value of 32 ft/sec2 or 9.8 m/s2.  To just get typical force, just disregard the division by G or just change G to a value of 1.
 
 

Centrifugal G-Force Using RPM's (Easy Method Using
Units of Feet)

F = (0.01846531 N)2 R

    This equation is used to calculate centrifugal G-force when the number of revolutions per minute and the radius are known.. N is the number of circles (Fractional circles are included as a fraction.) made within one minute, while R is the radius.  This formula works only in units of minutes and feet.  This was derived using dimensional analysis.
 

Centrifugal G-Force Using RPM's (Easy Method Using
Units of Meters)

F = (0.03344638 N)2 R

    This equation is used to calculate centrifugal G-force when the number of revolutions per minute and the radius are known.. N is the number of circles (Fractional circles are included as a fraction.) made within one minute, while R is the radius.  This formula works only in units of minutes and meters.  This was derived using dimensional analysis.
 
 

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