Arduino Mega TIMER1 one second interval
Your timer configuration is ok so far. Never the less I recommend using the TIMER1_COMPA_vect interrupt vector instead of TIMER1_OVF_vect which has the advantage of better readability (in my oppinion) and TCNT1 doesn't have to be reset in the ISR (instead, OCR1A is just initialized with 62500 once in setup()). Therefore, TIMER0 has to run in CTC (clear timer on compare match) mode and WGM12 has to be set in TCCR1B.

The reason why seconds_passed is incremented twice is because you Serial.print(seconds_passed++) in instantSpeed(). Printing on the serial interface is damn slow and using it in an ISR is a no-go!