Kinematics Kinematics EquationsEquations

The main equations will be asteriskedNOTE: You will NOT be

expected to do this on a test, but it is important to know these equations come from somewhere and were not arbitrarily made up.

dv

t

Let’s start with what you know, the equation we use for constant or average velocity

Now rearrange and solve for displacement d vt

If I wanted that velocity to be an average velocity between two points, an initial and final velocity, what would you change?

d vt2

F iv vd t

Let’s start with another equation you know, the acceleration equation

F iv va

t

This can be

rearranged and set equal to vF

F iv v at

F iv v at

2F iv v

d t

Take

And substitute it into

2

i iv at vd t

2

i iv at vd t

Simplify the equation

2

2iv at

d t

1

2id v at t

21

2id v t at

F iv v at Take

Rearrange it so that it is equal to t

F iv vt

a

2F iv v

d t

F iv vt

a

Now substitute it into

2F i F iv v v v

da

You should get this

Now simplify

1

2 F i F id v v v va

again

2 22 F F i F i iad v v v v v v

And again

2 22 F iad v v

The final form should be

2 2 2F iv v ad

dv

t

AKA “blue equation”

F iv va

t

AKA “Orange Equation”

2F iv v

d t

AKA “red equation”

21

2id v t at

2 2 2F iv v ad AKA “Light Green Equation”

AKA “Dark green Equation”

Using these Using these equationsequations

• There are a total of five (5) variables that are used in combination in these equations: vF, vi, a, t and d.

• You choose the equation based on what variables you have and which you need.