(YouTube link)
What would have happened at the end of the movie Back to the Future if Doc had overshot his target while traveling into the future? -via Unique Daily
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As for your second point, well yes the car probably shouldn't be able to punch through the hull of the Enterprise. But...fact is I don't consider these as being flaws at all. My video is a joke, not a physics lesson. If I tried to account for these in the production of my video, I wouldn't have been able to make it at all, let alone make it funny. Indeed the humor lies in the very absurdity of the whole scenario. Eliminate the absurdity and I'd be sitting at about 30 views instead of over 100,000 and counting.
As well, even with shields down, surely a Delorean going 88 MPH wouldn't be able to punch a hole all the way through a spaceship.