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Dynamics
A = B = 0
For the case A=B=0
we are left with the differential equation given by
dv/dt = -g
which has the well-known solution for an object which moves freely
in the vertical direction under the influence of the gravitational
attraction near the surface of the Earth
v = v(t) = v0 - gt
Here v0
represents the velocity at the instant of time
t=0:
v(t=0) = v0 - g×0
= v0
which has to be measured in
experiment.
Since the velocity v=v(t)
is given by the time derivative of the position
y=y(t) of the object,
v=dy/dt,
the above expression for the velocity leads to
the following equation for the height of the object:
dy/dt = v(t) = v0 - gt
Its solution is given by
y = y(t) = y0
+ v0t -
gt2/2
where y0
represents the height of the object at the instant of time
t=0:
y(t=0) = y0
+ v0×0 -
g×02/2
= y0
which has to be measured in
experiment.
A graphical representation is shown at the next page.
graphical representation