Distance and displacement

Distance is a scalar quantity representing the interval between two points. It is just the magnitude of the interval.  Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.

The SI unit for distance and displacement is m.

Distance here will be = 4m + 3m + 5m = 12 m

Distance Formula: Δd= d₁ + d₂  

Displacement is defined as the change in position of an object. It is a vector quantity and has a direction and magnitude. It is represented as an arrow that points from the starting position to the final position. 

For example- If an object moves from A position to B, then the object’s position changes. This change in the position of an object is known as displacement.

Look at the picture above, boy travels from D to A, A to B, B to C and C to D. Displacement from D to D (which are our initial and final points) is zero. However, distance traveled is not zero. It is equal to the perimeter of the rectangle.

_{Images: Harrage, E. (2023). Distance and displacement (CC BY)}

John walks from the point A to B to C. What does the distance he travel? 

What is the displacement?

Distance travelled:  He travels from A to B to C. Distance from A to B is 4 m and B to C is 3 m. Their sum will give us total distance:

4+3=7 m

Then it’s time to calculate displacement. Displacement is a vector quantity. So it must have both magnitude and direction. In this example the initial point is A and the final point is C.

Displacement vector is an internal between the initial and final points. As shown in the diagram the interval between A to C is 5 m. So, the displacement vector is 5 m and the direction is from the point A to C.

Image: LibreText Physics. (2022). Displacement (CC BY 4.0)

A passenger moves from his seat to the back of the plane. His location relative to the airplane is given by Χ . The −4.0 m displacement of the passenger relative to the plane is represented by an arrow toward the rear of the plane. Notice that the arrow representing his displacement is twice as long as the arrow representing the displacement of the professor (he moves twice as far).

Note that displacement has a direction as well as a magnitude. The displacement is 4.0 m toward the rear. 

In one-dimensional motion, direction can be specified with a plus or minus sign. When you begin a problem, you should select which direction is positive (usually that will be to the right or up, but you are free to select positive as being any direction). 

The airplane passenger’s initial position is x₀=6.0 m and his final position is  x_f=2.0 m, so his displacement is:

Δx=x_f−x₀=2.0 m−6.0 m=−4.0 m.

His displacement is negative because his motion is toward the rear of the plane.

Look at the picture given below. An object moves from point A through B, C, D, E and stops at point F.

a) Find final displacement.

b) Find distance taken from point A to D.

We find final displacement by drawing straight line from point A to final point F. As you can see from the graph, object changes its position 8m.

Displacement = Final position - Initial position Displacement = 10m - 2m = 8m

b) We find distance taken by object: 

A to B =10 - 2 = 8 m 

B to C = 10 - 2 = 8 m 

C to D = 10 - 6 = 4 m. 

Total distance taken from point A to D is = 8 m + 8 m + 4 m =20 m