How to make the motor move after a certain period of time?
You will need to add a logic level mosfet of the appropriate size and specs to control the power to the motor.  You can drive the gate of the mosfet from a pin through a current limiting resistor with a larger bleed resistor.  For a brushed motor you'll need a ceramic RF supressor cap plus flyback diode for back EMF protection:







simulate this circuit &ndash; Schematic created using CircuitLab

For greater RF supression (if your motor is pretty beefy) you can use a 0.1uF between each input lead and the motor case.

When you turn the pin on, motor turns on, low turns off.  Using analog and appropriate R values you can control motor speed (setting 0-255):

int motorControl = [your pin];

void setup()
{
  pinMode(motorControl, OUTPUT);
}

void loop()
{
  delay(10000); // delay 10 seconds plus board boot time
  analogWrite(motorControl, 255); // turn motor on full
}


You can time the delay with a stop watch and adjust to be exactly 10s by dropping the delay() call to compensate for the boot up time of the board.

More about MOSFETS here:

https://electronics.stackexchange.com/questions/81935/mosfet-usage-and-p-vs-n-channel