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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