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the 3rd kine eqns, p3
Rearrange of (I5) will produce
2
a
(
x
−
x
0
)
=
(
v
0
+
v
)
(
v
−
v
0
)
(
v
+
v
0
)
(
v
−
v
0
)
=
2
a
(
x
−
x
0
)
v
2
−
v
0
2
=
2
a
(
x
−
x
0
)
v
2
=
v
0
2
+
2
a
(
x
−
x
0
)
,
(I6)
\tag{I6} \begin{array}{rcl} 2a(x - x_0) & = & (v_0 + v)(v - v_0) \\[0.5em] (v + v_0)(v - v_0) & = & 2a(x - x_0) \\[0.5em] v^2 - v_0^2 & = & 2a(x - x_0) \\[0.5em] v^2 & = & v_0^2 + 2a(x - x_0), \end{array}
2
a
(
x
−
x
0
)
(
v
+
v
0
)
(
v
−
v
0
)
v
2
−
v
0
2
v
2
=
=
=
=
(
v
0
+
v
)
(
v
−
v
0
)
2
a
(
x
−
x
0
)
2
a
(
x
−
x
0
)
v
0
2
+
2
a
(
x
−
x
0
)
,
(
I6
)
which is the third kinematics equation.