Question

If the vertical axis and time on the horizontal axis if the speed is steadily increasing could the speef line ever become perfectly vertical

Answer 1

A graph of real speed can have a section that's as steep as you want,
but it can never be a perfectly vertical section.

Any vertical line on a graph, even it it's only a tiny tiny section, means
that at that moment in time, the speed had many different values.

It also means that the speed took no time to change from one value to
another, and THAT would mean infinite acceleration.