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the 3rd kine eqns, p1
First two equations, with
v
=
v
(
t
)
v = v(t)
v
=
v
(
t
)
and
x
=
x
(
t
)
x = x(t)
x
=
x
(
t
)
, are
v
=
v
0
+
a
t
,
(I1)
\tag{I1} v = v_0 + at,
v
=
v
0
+
a
t
,
(
I1
)
x
=
x
0
+
v
0
t
+
1
2
a
t
2
.
(I2)
\tag{I2} x = x_0 + v_0 t + \tfrac12 a t^2.
x
=
x
0
+
v
0
t
+
2
1
a
t
2
.
(
I2
)
Turn (I1) into following
t
=
v
−
v
0
a
.
(I3)
\tag{I3} t = \frac{v - v_0}{a}.
t
=
a
v
−
v
0
.
(
I3
)
and then substitute to (I2)