Jerk problem, race car weight transfer

If there is a mass with 1G force in one direction and a opposing linear changing force from 0 at the start to a equal force to the 1G when motion stops. The only other info known is a displacement of .146′. If I could calculate the jerk ,which should be constant, I will know time and have a slope for acceleration. The velocity curve should start at 0 have a max at center on the time axis then go back to 0. All the derivatives to jerk, require time, which is not given. The more I think about this maybe the opposing force is not linear because the velocity is greater in center causing a quicker change in force
From the opposing spring being compressed more rapidly. This would make the acceleration plot be nonlinear. Can this be solved with what is known if acceleration change was linear?
This problem pertains to the center of gravity of the sprung mass rotating around the roll center with lateral centripetal force acting on it. I am not sure this is really how it works because entering a turn the sprung mass of the car is attempting to stay where it was and the tires and axle are changing its direction.