Provide all the details you have... The exact motor (datasheet link if possible), its driver (datasheet link if possible), power supply, how its all connected (full circuit diagram is possible).
When you say "1600 pulses = 1RPM" do you actually mean "1600 pulses per revolution" ? And its not clear if you want to change this ratio, provide more pulses per second, or what... You perhaps should break down your problem into separate issues (analogRead and potentiometer is one, driving the motor is another).