Accelaration problem

My 2001 Chevy Blazer seemed sluggish yesterday when I accelerated. Today, when I would accelerate nothing would happen for several seconds even with the accelerator pushed to the floor, then the RPMs would go through the roof and the car would slowly begin to accelerate. The car would get up to speed, then this cycle would happen again. Any ideas about what I need to check out?

Check your transmission fluid. Make sure it is full, and if it is, smell the dipstick. It should smell like nothing. It should also be pink and clear.
Hopefully, the fluid is low and you have a leak somewhere that needs to be found and fixed eventually but for now you just need to add the correct transmission fluid for your Blazer.

But if the fluid smells burnt, you need a new tranny.

If nothing would happen for several seconds then it is unlikely to be the transmission. Unless by “nothing would would happen” you just mean that the truck wouldn’t go, but the engine revved up really high.

So clarify. If you pushed the pedal to the floor and RPMs just sat there flat down around idle then it is an engine control problem.

If you pushed the pedal to the floor and the RPMs went up as soon as you pushed the pedal but it took several seconds to actually get any locomotion - then you’re probably looking at the end of the transmission.

To me anyway, this is interpreted as the transmission not moving the vehicle and you should check the transmission fluid.
If the fluid is brown or black then you can assume with a very high degree of certainty the transmission is fried.