A car travels 5km to east. Then it goes 3km to north and then 2km to west. What is the displacement the car has traveled?

(5-2) = 3 km east, and

3 km north.
The displacement is 3*sqrt2 km, in a NE direction

To find the displacement, we need to determine the straight-line distance between the initial and final positions of the car.

Given that the car traveled 5 km to the east, followed by 3 km to the north, and then 2 km to the west, we can represent its path graphically:

----------
| 3
| ↑
| |
2 |5 ← C ←--- B
| ↓
----------

To find the displacement, we can consider the x-axis as east-west, and the y-axis as north-south.

The initial position is at point A, where the car starts.
The final position is at point C, where the car ends up after traveling.

To determine the displacement, we need to find the horizontal and vertical components separately, and then combine them using the Pythagorean theorem.

Horizontal component (horizontal displacement) = distance traveled to the east - distance traveled to the west
= 5 km - 2 km
= 3 km to the east

Vertical component (vertical displacement) = distance traveled to the north - distance traveled to the south
= 3 km - 0 km
= 3 km to the north

Now, we can calculate the displacement using the Pythagorean theorem:
Displacement = √(horizontal component)² + (vertical component)²
= √(3 km)² + (3 km)²
= √9 km² + 9 km²
= √18 km²
=~ 4.24 km (rounded to two decimal places)

Therefore, the displacement of the car is approximately 4.24 km.

To find the displacement of the car, we can use a coordinate system. Let's assume the starting point of the car as the origin (0,0).

First, the car travels 5km to the east, which means it moves 5 units in the positive x-direction. The new position of the car is (5,0).

Next, the car goes 3km to the north, which means it moves 3 units in the positive y-direction. The new position of the car is (5,3).

Finally, the car moves 2km to the west, which means it moves 2 units in the negative x-direction. The new position of the car is (3,3).

To calculate the displacement, we need to find the straight-line distance between the starting point and the final position. We can use the Pythagorean theorem to calculate this.

The displacement (d) is given by:
d = √((Δx)^2 + (Δy)^2)

In this case:
Δx = 3 - 0 = 3 (change in the x-coordinate)
Δy = 3 - 0 = 3 (change in the y-coordinate)

Substituting the values into the formula:
d = √((3)^2 + (3)^2)
d = √(9 + 9)
d = √18
d ≈ 4.24 km

Therefore, the displacement of the car is approximately 4.24 km.