DC Motor very high acceleration
In an ideal DC motor, rev is proportional to voltage and torque proportional to the current. So if you connect it to a constant-voltage supply, it would ideally reach the maximum speed immediately. Of course, this does not happen in reality: the mechanical parts have a finite moment of inertia, so you get an increase of angular momentum -> torque -> current, which would be infinite for an immediate-response. Such a current is prevented by two factors:


a non-arbitrarily powerful supply,
the internal resistance of the copper wire inside the motor.


Assuming you have an over-sufficiently powerful supply, you can also overcome the latter factor to some degree: the voltage that drops off at the copper resistance simply follows Ohm's law. You can determine the resistance \$R\$ by applying a small voltage to the motor while this is blocked mechanically. Then, rather than simply using the constant voltage that corresponds to the desired rev in torque-free mode, you always add the voltage \$R\cdot I\$. You need to be careful not to produce resonances with such a feedback circuitry. Also, not all motors might cope very well with the large currents that may arise with this method.