If it’s an older model car, this sounds like a fuel starvation problem.
Check your fuel lines for leaks.
Check your air filter: if it’s very dirty, replace it.
Buy a kit for the carburetor and once you have replaced everything, check that the float level is correct.
READ ALSO: THE IMPORTANCE OF TIRE PRESSURE IN CARS
Ensure that the carburetor is properly torqued down and that no air gets in between it and the inlet manifold. Use an approved gasket sealant on the gasket between carburetor and manifold.
Ensure that the ignition timing is correct for your particular altitude. Use a timing light to set it.
If the timing is correct but the car still experiences hesitant and/or jerky acceleration, check that the ignition coil is supplying the correct voltage. A weak or shorted coil can’t supply a strong enough spark and results in poor combustion in one or more cylinders. Check and replace spark plug wires with corroded contacts and/or cracked or frayed insulation.
Spark plugs will not function well when choked with carbon deposits. Remove the spark plug and clean the spark gap area with a wire brush and cleaning solution. Measure the gap and adjust if necessary before reattaching the spark plug.