Facepalm MK.3 *Sigh* In the history of Trek I've NEVER seen the Federation transport a ship and I'm not even going to touch acts of Q. While I can easily accept the possibility of the alternate universe part Never have i seen the Federation have the capability of sending a whole star ship through at once.
They wouldn't need to transport a ship. Just the people would get transported to somewhere like Terok Nor in the mirror universe. I wasn't even thinking about using the transporter to transport a ship. The only time I remember seeing that done is by the Voth city-ship in voyager episode "Distant Origin".
I'm assuming for this that they use an impulse drive like everyone else. Voyager has previously been said to have max impulse speeds of between .66c and .8c, although this is from Memory Alpha so someone with the episodes / movies handy might want to check them for accuracy. I've never heard of figures being given for accelerating though.
One other thing to bear in mind is that some impulse drives at least may use mass lightening to move around, which will make any such impact less dangerous. And yes, I realise that whatever the Borg cube was trying to ram would not be acting like a sitting duck
you know a species 8472 bioship is capable of destroying a borg cube in one or two hits. This didn't save them from being collided with.
Here's a low estimate figure on how fast a borg cube can go:
In episode "once upon a time", the delta flyer had taken heavy damage from an ion storm but tom paris felt that they could outrun an ion storm traveling at 33,000 kph with their thrusters if they had more power. Keeping in mind that the delta flyer was damaged and probably couldn't travel at its optimum speed here.
In voyager episode "collective" the delta flyer was unable to outrun a weakened borg cube which only had a few children on it. A borg cube with thousands of drones on it would undoubtedly be able to go faster than this. But we can at least say that a borg cube should be able to go faster than 33,000 kph which isn't anywhere near the speed of light but still pretty fast by today's standards. If that's not enough to destroy a star destroyer I can look for something else.