Newtonian analogue of force and motion of a free particle in the gravitational field of theC-metric

In the first part of the paper the Newtonian analogue of force for theC-metric has been investigated. To the first-order of approximation in the absence of acceleration of the particle generating theC-metric, one component of the force vector corresponds to the Newtonian analogue of force. In general there are relativistic correction terms due to acceleration term in theC-metric. In the second part of the paper the motion of a freely falling body has been investigated. It is found that plane orbits are not possible. Also the radial fall is not possible and in the equation of the orbit there are terms having no classical analogue. They can be interpreted as the effect of the dragging of the inertial frame produced by the rectilinear acceleration.