Distance and Displacement

Distance: The length of any path traveled by an object is called distance. Distance is a scalar quantity because it only has magnitudes, no directions.

Displacement: The shortest distance from the initial and final position of the object that it traveled is called displacement. Displacement is a vector quantity because it has both magnitudes and directions.

However, distance and displacement are measured in the same unit which is centimeter(in C.G.S) and meter( in S.I). Because both of them are the measure of length.

Understanding Distance and Displacement

Distance and Displacement in 2-Dimensional linear path:

Suppose you are traveling in a 2-Dimensional linear path( in the given figure). Your initial position is marked by A. If you first reach position B, and then C, the distance you travel is as follows

But the displacement will be the shortest distance from the initial position A to the final position C. So the displacement you will get is the straight-line AC, which is shown in the picture with the green line.

This can be measured by applying the Pythagoras theorem. Here ABC is a right triangle so the hypotenuse of this triangle is displacement and its measurement is as follows

Distance and Displacement in 2-Dimensional circular path:

Now suppose you are traveling in a circular path( in the given figure). Your initial position is marked by A. If you reach position B first, the distance you will travel will be half of the perimeter of the circular path.

Where the displacement will be the diameter of the circular path. Because the shortest distance from A to B is the diameter of the circular path.

Now again if you come back to the initial position where you start your journey or if A becomes your final position then the distance you will travel will be the perimeter of the circular path.

Where the displacement will be zero. Because there is no separation between the initial and final position. So there is no shortest distance between them.

So in the first case:

If R is the radius of the circular path

Distance = 𝜋R (Half of the perimeter of the circular path)

Displacement = 2R (Diameter of the circular path)

And in the second case:

Distance = 2𝜋R (Perimeter of the circular path)

Displacement = 0

So distance and displacement mean the same thing but still have different definitions and meanings. Similarly, speed and velocity mean the same thing but have different definitions and meanings. To know more