$\therefore $ $\frac{{da}}{{dt}} = k$ (constant) $⇒$ $a = kt$ (by integration)

$⇒ \frac{{dv}}{{dt}} = kt$ $⇒$ $dv = ktdt$

$⇒ \int_{}^{} {dv} = k\int_{}^{} {tdt} $ $⇒$ $v = \frac{{k{t^2}}}{2}$

i.e. $v$ is dependent on time parabolically and parabola is symmetric about v-axis.
and suddenly acceleration becomes zero. i.e. velocity becomes constant.

Hence $(c)$ is most probable graph.