Yes. usually we name them $a'$ . and there can be even a speed of my $a'$ that I can call that $a''$ and it goes on like that.
it is only used it real life calculation that the calculation should be very precise like rocket science.
and the equation of displacement (with a constant $a'$) will be :
$$x =\frac16 a't^3 + \frac12 a_0t^2 + v_0t+x_0$$
(EDIT: also should mention sometimes they put a little dot on the a too instead of apostrophe )