A car travels 3 km north, then turns and travels 4 km west. What is the car's
displacement?

"Displacement" is the straight-line distance and direction between the start-point and the end-point, regardless of what route was taken to get there.

If you draw a picture of how this car traveled, you'll see that it drove along two legs of a right triangle. I'm guessing the driver probably decided to stay on the streets, instead of driving the STRAIGHT line across people's lawns to get to the grocery store.  if a BIRD wanted to make the same trip, it would just fly in a straight line, straight over houses and yards.

The bird would fly along the hypotenuse of the right triangle.  The distance would be  √(3² + 4²).

That's √(9 + 16), which is √(25), and that's 5 km .

'Displacement' is a vector, and it also needs a direction.

After driving 3km north and 4km west, you are 5km roughly Northwest of where you started from.  (actually 53.1° west of north)

The car's displacement is 5 km , 53.1° west of north,

or 5 km at an azimuth of 306.9° .