In practice there is no such thing as "a slow asteroid hitting".
There are only "too damn fast" and "even faster". The MINIMUM
impact speed we can plausibly expect is escape velocity, and this is
assuming that the body's former orbit nearly amounted to a docking
maneuver with Earth -- any variation from that will either *increase*
the impact speed, or prevent a collision.
Now a slow collision with an aeroshell manufactured in orbit from
asteroidal materials, is a completely different matter...
Another factor to consider is that there are some potential orbital
hazards that are easy to spot because they are in only mildly
elliptical orbits and don't get much further from the sun than the
earth does. And there are others that are much harder to spot
because they are in seriously elliptical orbits and spend most of
their time substantially further from the sun (i.e. less well lit).
These latter bodies also have the interesting characteristic that
they are much more likely to *not* orbit in the plane of the ecliptic
(or anywhere near it), so they are more likely to come from a totally
unexpected reaction.
And for the real kicker: they'll be moving a *lot* faster when they
cross earth orbit.
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