What causes a car to hesitate when it accelerates?
Fuel injected cars have several sensors monitoring engine rpm,
engine load, speed and throttle position allowing a computer to
decide the correct amount of fuel for smooth acceleration..
Carbureted cars have the throttle connected more directly and
simply dump fuel whenever the pedal is pressed, simple but
ADDED: The answer is a little more complicated than the 2nd
scenario and would take up much more space to explain. Suffice it
to say that you should try running a can or two of carburetor
cleaner through it via the gas tank, AND get a spray can of carb
cleaner and thoroughly spray down the throttle linkage where it is
mounted on the side of the carb to make sure that everything moves
smoothly. See what happens after you've done this, and if it still
is exhibitting the same problem take it to a mechanic that still
knows how to work on and/or adjust carburetors, because iyou could
have internal problems that might require a rebuild.
Not enough fuel, maybe because the fuel pump is not putting out
enough pressure, or more likely and cheaper. Replace the fuel
filter that is just above the transmission on the firewall.