Dc motor, PIR Sensor, speed controller - is it possible ?

Hi, good people.
I am trying to make an installation in which a PIR Sensor triggers a dc motor every time there is movement. I want the dc motor to be turned on for three minutes. In those three minutes I want the motor to stop every 20 sec, for 20 sec. Is it at all possible. For instance with a speed controller. Sorry if it it a stupid question, this is my first time using an Arduino.
Thanks in advance.

Yes, easy to do.

byte pirPin = 2;
byte motorPin = 3;
byte motorState = 0;
byte x;

void setup(){
pinMode (pirPin, INPUT_PULLUP); // assumes open-collector type that pulls the pin low when active
pinMode (motorPin, OUTPUT); // assume pin drive a transistor base (NPN) or gate (N-channel MOSFET)
                                                  // high to sink current through a  motor
void loop(){
if (digitalRead(pinPin) == LOW){
for (x=0; x<9; x=x+1){
motorState = 1 - motorState; // so 1-0-1, 0-1-0, 1-0-1
digitalWrite (motorPin, motorState);
delay (20000); // dumb delay, there are smarter ways to do this
digitalWrite (motorPin, LOW); // turn off at end

Hi thanks a lot.
I am really happy that it is possible, I actually just copy pasted the code that you sent me to see how it worked, and this message popped up 'pinPin' was not declared in this scope. How can i fix this problem ?

Just change pinPin to pirPin at following line;

if (digitalRead(pinPin) == LOW)

Will be

if (digitalRead(pirPin) == LOW)