Equations for linear motion and dynamics problems
(i.e. position, velocity, acceleration, time, force)


Here is the basic set of equations for solving linear motion problems as well as the relevant units to use in the calcs. The equations are organized into the fundamental ones, main derivatives, and other forms that might be of help. This is the simple version of this- no complicated differetial equations to puzzle over or strange characters to decode. Reference urls, and even a calculator that solves these problems is provided at the end.

Index of abbreviations used:

Xo = starting position
Xf = final position
D = distance from start
T = time in seconds
V = velocity at specific time or position
Vo= starting velocity
Vf= final velocity
A = acceleration
F = force
M = mass


Units for motion / dynamics problems: (length, mass, time, force)

MKS:
meters, kilograms, seconds, newtons (newton = weight in kilos / 9.81)

CGS:
centimeters, grams, seconds, dynes (one dyne = 0.00001 newton)

"English" system:
feet, slugs, seconds, pounds (slug = weight in lbs / 32.2)

Important: Pick one system and convert all units to same system / set. Don't mix or messes will result.


The fundamental equations of linear motion (kinematics)

1. V = (Xf - Xo) / T (this is average velocity)

2. A = (Vf - Vo) / T (this is average or constant acceleration)

 

The fundamental equation of dynamics

3. F = MA

Deriving from the above produces the ones we actually use.


The full equation of linear motion (the one to memorize and not forget)

D = Xo + VoT + 1/2AT^2


The four basic equations of motion assuming constant acceleration

1. V = Vo + AT

2. D = 1/2 (Vo + Vf)T

3. D = VoT + 1/2AT^2

4. V^2 = Vo + 2AD

The four basic equations of motion assuming constant acceleration and zero initial velocity (i.e. dragracing)

1. V = AT

2. D = 1/2VT

3. D = 1/2AT^2

or T = sqrt(2D/A)

4. V = sqrt(2AD)

or V = sqrt(2F/M * D)

or V = sqrt (2AT^2)

or V = sqrt (2F/M * T^2)



Kinetic energy or power

K = 1/2 MV^2

 


References:

Motion equations:
http://en.wikipedia.org/wiki/Equation_of_motion#Motion_Equation_1
http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html#mot1 (with calculator)
http://zebu.uoregon.edu/~probs/glossary/Equations/Equations.html

Units:
http://scienceworld.wolfram.com/physics/MKS.html