Is it possible to connect up two electric motors in such a way that when the power is increased, the speed of one of the motors increases exponentially compared to the other. eg;
current 1 amp motor1 =10 rpm motor2 =10 rpm
current 2 amp motor1 =20 rpm motor2 =40 rpm
current 3 amp motor1 =30 rpm motor2 =90 rpm
current 4 amp motor1 =40 rpm motor2 =160 rpm
Firstly, power is not Amperes. Power is the product of Amps time Volts, which gives Watts.
Now to your question - yes, it could be possible. If you connect a low voltage motor ( A ) and a lower voltage motor ( B ) as you describe, then increasing the voltage will make B go faster than A, until B burns out / blows up!!
Speed is equal to Frequency (hz) / pairs of poles.
As you can't change the number of poles in the motor (without major overhaul), only way to change speed is to change the frequency (eg 50Hz to 60Hz)