How do I realize this problem with a digital circuit?
Here's a circuit that'll give you a 2Hz output whenever a speed threshold is exceeded and will continue to output 2Hz as long as the threshold is exceeded.

Here's how it works:

U1 is a 555 wired as an astable multivibrator with a period of about 1/2 second, with its RESET input controlled by U2, a voltage comparator.

A voltage comparator works by having its output go high when its + input is more positive than its - input, and in this case I've chosen the voltage on the - input to be half of the supply voltage by connecting it to the junction of R1 and R2, a voltage divider comprising two resistors with equal values.  For the purpose of this exercise, I set the supply voltage (12 volts) to be equal to 120 miles per hour and to vary linearly from zero MPH with U2- equal to zero volts, to 120 MPH with U2- equal to 12 volts.

Thus, with U2- sitting at 6 volts, the speed detection threshold is set at 60 MPH.

The voltage on U2+ comes from V1, which is the output voltage from the pot you mentioned earlier, and varies linearly from zero to 12 volts, corresponding to a vehicle speed of from zero to 120 MPH. 

With the voltage on U2+ lower than the voltage on U2-, then,  U2's output will be low and will keep U1 RESET, forcing U1-3 low. 

As the vehicle speeds up and V1's output goes more and more positive, eventually it'll get more positive than the 6 volt reference on U2-, which will cause U2's output to go high, taking U1 out of RESET and allowing it to oscillate at about 2Hz, giving you the output you want for your counter. 

So, When the vehicle's speed is higher than 60 MPH U1 will oscillate, but when it's lower than 60MPH, U1 won't do anything.

Self-help 555 and comparator tutorials are all over the web, so I won't go into them here but, if you're interested, there's a nice, free simulator program here, and I've posted the schematic as a file which you can run to play with the circuit here.