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...

\begin{large}\[ v_{f} = v_{i} + a(t_{f}-t_{i})\]\[x_{f} = x_{i} + \frac{1}{2}(v_{f}+v_{i})(t_{f}-t_{i})\]\[x_{f}=x_{i}+v_{i}(t_{f}-t_{i})+\frac{1}{2}a(t_{f}-t_{i})^{2}\]\[v_{f}^{2}=v_{i}^{2}+2a(x_{f}-x_{i})\]\end{large}

It is clear from these equations that there are seven possible unknowns in a given problem involving motion between two points with constant acceleration:

...

Because

the

initial

position

and

initial

time

can

generally

be

arbitrarily

chosen,

it

is

often

useful

to

rewrite

all

these

equations

in

terms

of

only

five

variables

by

defining:

\begin{large}\[ \Delta x \equiv x_{f}-x_{i} \]\[\Delta t \equiv t_{f}-t_{i}\]\end{large}

then

each

of

the

equations

given

above

involves

exactly

four

unknowns.

Interestingly,

the

four

equations

represent

all

but

one

of

the

unique

combinations

of

four

variables

chosen

from

five

possible

unknowns.

Which

unique

combination

is

missing?

Can

you

derive

the

appropriate

"fifth

equation"?