  Referring to the behavior of accelerating objects in special relativity, and
applying the principle of equivalence, one expects that the coordinate
acceleration of point masses under gravity will be velocity dependent. Then,
using the Schwarzschild solution, we analyze the similar case of masses moving
on timelike geodesics, which reproduces a little known result by Hilbert from
1917, describing this dependence. We find that the relativistic correction term
for the acceleration based on general relativity differs by a factor of two
from the simpler acceleration arguments in flat space. As we might expect from
the general theory, the velocity dependence can be removed by a suitable
coordinate transformation, such as the Painlev{\'e}-Gullstrand coordinate
system. The validity of this approach is supported by previous authors who have
demonstrated vacuum solutions to general relativity producing true flat space
metrics for uniform gravitational fields. We suggest explicit experiments could
be undertaken to test the property of velocity dependence.
