How to form Kalman filtering matrices for a problem with variable acceleration?
Take the first model and train your model noise matrix $\bf{Q}$ to account for the variable acceleration. A popular model is the Singer model from 1990 (see [1]).

[1] Singer, R. A., “Estimating Optimal Tracking Filter Performance for Manned Maneuvering Targets,” IEEE Transactions on Aerospace and Electronic Systems, vol. AES-6, no. 4, .pp. 473-483, July 1990.