The velocity
v of the particle
is given by the relation of its time derivative
to the acceleration.
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(
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)
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= dv/dt
= a =
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(
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)
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= -
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(
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)
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= - g
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The differential equation dvx/dt = 0
is solved by
vx
= v0x
v0x
represents the x component
of the initial velocity
v0.
The differential equation dvy/dt = -g
is solved by
vy
= v0y - gt
v0y
represents the y component
of the initial velocity
v0.
We end up with
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v(t)
=
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(
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)
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=
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(
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)
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-
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(
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)
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t
= v0
- gt
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