Usage of front and side

[daemon99]

Do the following sentences make any sense? Can someone please suggest better ones?

Assume we were in a car.
1) A big truck sped across in front of us.
2) A big truck came from the side, cut in on us and sped right ahead.

[Anglika]

They both make sense.

[daemon99]

Thanks a lot, Anglika!

Can the first sentence be rephrased to:

1) A big truck came at a great speed and crossed our path.

[Tdol]

Cut in front