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I think it must be Roadblasters. There's gameplay footage on Youtube that looks like what I remember.
I vaguely recalled a video game I played one time at Showbiz Pizza about 25 years ago, and I was able to write a description so someone on the Internet could identify it within hours. I find that weird to think about.
Anyway, thanks, Erica!

I played this once when I was pretty young, so my memory is vague and some of these details could be wrong. It was an arcade game in the late '80s. It was a racing game much like any other, except one thing made it memorable. Every so often a pair of laser cannons would come down from the sky and attach to your car, allowing you to blast away obstacles.