Question

One Dimensional Kinetics - Non-constant Acceleration Challenging Problems 1.

If anyone also worked on this problem. I would like to hear your thoughts. The solution has Time-final at the point where the non-constant acceleration and the constant acceleration velocities first meet. What is the fuel allows the non-constant acceleration to burn further pass the first interaction after time zero? such that the non-constant acceleration velocity will be higher than the constant acceleration velocity. The average velocity for the nonconstant acceleration may can be higher than Vf/2. thought?