How to find the coordinate of final point in a parabolic motion through 3 points where 2 points are known?

Question

Suppose an object travels in a parabola in 2D coordinate system from P to Q and then Q to R where the 2D coordinates of P and Q are known and we do not know the parabola through these 3 points.

The object goes from P to Q in 1 millisecond and Q to R in 2 millisecond.

Is it possible to calculate the 2D position of R? If yes how can I find that? If no why not?

Answer 1

Based on how you pose your question, the answer is no. Why? You don't have enough information. What information is missing? What is the force influencing the behavior of the object?

EDIT TO RESPOND TO COMMENT:

In that case, F = ma is not the way to go. You are talking Kinematics. You need to research Kinematics and Jacobian matrix/determinant. This will solve your problem.