Arduino LED strobe light with a MOSFET
what is the source voltage?  In your diagram, you have +5 to +24 V feeding into a motor...  You mentioned car power, and an arduino - so I'm guessing you're either supplying ~ 12V or 5V; also, are you driving the output high/low?  Or is it setup to be open source?

And, are you sure that your city still uses strobed IR bulbs without a special pattern to control its traffic lights?