  We investigate the dynamics of an Airy pulse that experiences free carrier
generated optical linear potential in the vicinity of zero group velocity
dispersion (GVD) wavelength inside a Si based waveguide. The optically induced
potential can be realized by an inhomogeneous medium which possesses a time
dependent refractive index. We propose a pump-probe scheme in Si-based
waveguide where a strong continuous wave (CW) pump excites free carriers that
leads to a linear potential through a time dependent refractive index change
which is experienced by the finite energy Airy pulse (FEAP) (probe). The linear
potential significantly manipulate the dynamics of a FEAP and leads to a
monotonous spectral shift. We mathematically model the dynamics of the Airy
pulse using linear dispersion equation containing an optical potential term and
establish the general solution of the pulse for non-vanishing third order
dispersion (TOD). We derive the expression of the trajectory of FEAP which
deviates significantly from its usual ballistic nature and can be tailored with
the strength of the linear potential. For positive TOD, the propagating Airy
pulse experiences a singularity and flips in time domain. We theoretically
derive that for a specific potential strength the flipping region is squeezed
to a point and revives thereafter. We propose an exact analytical solution
beyond flipping region for this specific case. Our theoretical analysis
corroborates well with the numerical results. The present study may be useful
in applications related to pulse reshaping and trajectory manipulation
