Finding relativistic force in terms of acceleration

[SquidgyGuff]

Homework Statement

The instantaneous force F acting on a particle, as measured in frame S, is

Use the formula for the linear momentum (

) in and the definition of the acceleration a to show that

The Attempt at a Solution

The professor said that this required use of programs such as mathematica in order ot solve, however, I can't figure out a way to solve this, I can derive the force transformation into another inertial reference frame, but the equation needs to be in terms of acceleration in the S frame, not the S' frame. I just need to know where to start with this.

 

[Geofleur]

It looks like you will need to treat ## \mathbf{u} ## and its magnitude as functions of ## t ## and take the time derivative of the expression given for ## \mathbf{p} ##.

 

[SquidgyGuff]

It looks like you will need to treat ## \mathbf{u} ## and its magnitude as functions of ## t ## and take the time derivative of the expression given for ## \mathbf{p} ##.

Is there anyway to do this without expressing u in terms of t? In the prevoud question I found the velocity transformation as follows: