motion of particles under pseudo-deformation

In this short article, we observe that the path of particle of mass m moving along r = r(t) under pseudo-force a(t), t denotes the time, is given by rd = ʃ ( dr/dt a(t))dt + c. we also observe that the effective force fe on that particle due to pseudo-force a(t), is given by fe = fa(t) + lda(t)/dt, where f = m d^2r/dt^2 and l = m dr/dt. we have discussed stream lines under pseudo-force.