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kinematics, integrate a to v
Integrate acceleration
a
a
a
to obtain velocity
v
v
v
v
(
t
)
−
v
(
t
0
)
=
∫
t
0
t
a
(
τ
1
)
d
τ
1
.
(E1)
\tag{E1} v(t) - v(t_0) = \int_{t_0}^t a(\tau_1) d\tau_1.
v
(
t
)
−
v
(
t
0
)
=
∫
t
0
t
a
(
τ
1
)
d
τ
1
.
(
E1
)
Initial condition
v
(
t
0
)
=
v
0
v(t_0) = v_0
v
(
t
0
)
=
v
0
, will give
v
(
t
)
=
v
0
+
∫
t
0
t
a
(
τ
1
)
d
τ
1
.
(E2)
\tag{E2} v(t) = v_0 + \int_{t_0}^t a(\tau_1) d\tau_1.
v
(
t
)
=
v
0
+
∫
t
0
t
a
(
τ
1
)
d
τ
1
.
(
E2
)