The force acting on the mass at t=0 can't be determined without additional information such as the function r(t) or information about the applied forces at that specific time point.
To determine the force acting on a mass at a specific time t=0, it is essential to have information about the position function r(t) that describes the particle's path. The force acting on an object is related to its acceleration through Newton's second law, F=m⋅a, where m is the mass and a is the acceleration.
The acceleration can be found by taking the second derivative of the position function with respect to time, a(t)=r′′ (t). Without knowledge of the position function or the applied forces, the force at t=0 cannot be determined. Additional details about the system, such as the forces acting on the particle or the specific form of r(t), are required to calculate the force accurately.