Well pump cycles, presure switch on and off ,contacts keep breaking in the pressure switch
With a rapid on off cycling of the pressure switch the bladder has usually failed or lost its air charge.  (Bladder or diaphragm). 
Turn the power to the pump off and drain the water pressure open a spigot. 

Now use an air compressor , bicycle tire pump or some method to pump up the tank to ~38 psi.  There is normally a small valve like a tire valve stem on the top of the tank. This is where to add the air. If you leave the spigot open and air starts coming out or you can not pressurize to 38 psi the bladder or diaphragm has failed. 
If you stain 38 psi close the spigot and let the tank fill it should now cycle normally.  

On older diaphragm tanks that had failed I had charged them and the system will cycle close to normal but the charge will be lost if the water level in the tank gets low and over time the air dissolving in the water will require recharging but this may provide some time to save for a new tank I am not sure if a bladder tank will have enough volume for this to work but may be worth a try. 

I would not leave a system with a failed tank powered up as the rapid on off will damage the pump and the switch contacts along with creating a large number of voltage spikes that can damage sensitive electronics in the home.