12V LED Stripe with motion detector

Other Hardware LEDs and Multiplexing
1

Hey guys,
I know I know there are hundreds of threads about those 12V LED Stripes.... buut I#m kinda too dumb.
Okay so I want to put this LED Stripe onto my Grandmas stairway and connect it to a motion detector so that she has light when she goes to the toilet at night.
I'm not really sure. My Plan was to cut the Power Supply of the Stripe in half and put a 5V controlled Relay into the curcuit. Is this a stupid way? Or are there better ways?
I'm pretty okay with programming but I'm a electric noob.

Or is it smarter to directly connect the Strip to the Power and just put the Signal wire into the Arduino? If so, how can I do that? Like which Pin and so on

Hope you share your Ideas with me

2

This seems to have nothing to do with an Arduino.

Most full function PIR sensors such as the HC-SR501 already provide a persistence delay control so you only need to connect it to a relay module

However you can get one already set up to control your light strip.