I’m designing a circuit where a motor should turn ON for 15 seconds when the input voltage is between 2–3V. I'm using a npn and 2k base resistor and flyback diode to run the motor

 

Can 555 deliver enough current to the motor?

 

Sorry I did not read the last sentence of your post, I only saw the drawings.
To troubleshoot this you would have to begin with one of the ends... What I would first do is disconnect the motor and see if I still have the 15 second voltage where it should be... if yes the problem is something with the motor - if no, check the base of the output NPN.. and so on..

 

Welcome to AAC.

Is this an assignment for academic credit?

 

Use two separate power supplies. One only for the motor and another only for the comparator-timer-triggering-driver circuit.

 

you can derive "separate logic supply" by using diode and capacitor. the capacitor can be used as a buffer for brownouts caused by motor load

 

Use two separate power supplies. One only for the motor and another only for the comparator-timer-triggering-driver circuit.

I spent 2 days trying to debug the circuit, and this was the issue!!!! thanks is much for your help. and if I'm not mistaken this is because using one power supply for all my circuits doesn't provide enough current for the motor to run

 

I immediately suspected a supply voltage drop, based on them not working when both are connected. That is a frequent problem.