  We show that by manipulating the momentum (k) of a propagating optical pulse,
the intensity can be controlled and highly enhanced in a linear binary photonic
time crystal (PTC) system. The optical pulse equipped with k lying within the
bandgap of the PTC gets amplified and gives rise to reflected and transmitted
pulses with an equal growth in intensity moving in opposite directions. We
predict and quantify the amount of amplification of the transmitted and
reflected pulse and show the amplifications achieve a maximum at the centre of
the k-gap accompanied by weaker growth in intensity at the edges. The maximum
growth in the intensity of the optical pulses attains different values for
different ranges of k-gaps in such systems. Such precise control over the
amplification of propagating pulse can be exploited exclusively by tailoring
the wave vector of the pulse and open a unique platform for light manipulation
in futuristic unconventional active photonic devices.
