Distance and displacement are two important terms in mechanics that may seem similar but have different meanings. Distance is the total length of the path traveled by an object during motion, and it does not depend on direction.
Displacement is the change in position of an object. It is the shortest straight-line distance between the initial and final positions, along with direction. Hence, distance is a scalar quantity, while displacement is a vector quantity. The unit of both distance and displacement is meter (m).
Distance
Distance is the total path covered by an object in motion, regardless of the direction. It is a scalar quantity, meaning only the magnitude of the path length is considered, not the direction.
Distance is represented by the symbol 'd' and is not indicated with an arrow, as it is a scalar quantity and direction is not considered. The distance between points A and B is illustrated in the image below.
Distance Formula
Mathematically, distance is defined as the total length of the path traveled by an object from one point to another.
We know that,
Speed =\frac{ Distance }{Time}
Therefore using the above formula we get the formula for the distance when the speed and time of any motion is given is,
Distance = Speed × Time
\boxed{d= \, s \times t}
where,
- d is the Distance Covered by Object
- s is the Speed
- t is the Time Taken
Displacement
Displacement is defined as the change in an object's position, taking into account both magnitude and direction. It is a vector quantity because it includes both magnitude and direction from the initial to the final position.
Displacement is measured along the shortest straight-line distance between the initial and final positions. However, the object does not necessarily move along this straight path. The displacement between points A and B is shown in the image below.
Displacement Formula
Mathematically, the displacement is defined as, the "Minimum distance between two points." The formula used to find the displacement is,
\boxed {\Delta x = \, x_f - x_i}
where,
- xf is the Final Position of Object
- xi is the Starting Position of Object
- ∆x is the Displacement of Object
Distance vs Displacement
Distance is the total path covered by an object in motion, regardless of the direction, while Displacement is the straight-line distance between the initial and final position of the object, along with the direction of motion. The differences between Distance and Displacement are shown in the table added below,
Distance | Displacement |
|---|---|
| Distance is the total path covered by the object in motion, irrespective of the direction of the path. | Displacement is defined as the total change in the object's position along with the direction of motion. |
| Distance is a Scalar Quantity. | Displacement is a Vector Quantity. |
| When Distance is calculated, only the length of the path is considered, ignoring its direction. | When Displacement is calculated, both the length of the path and the direction of the object are considered. |
The distance covered is always positive | However, displacement can be positive, negative, or zero. |
Similarities
- SI unit of both Distance and Displacement is meter (m).
- Both distance and displacement depend on the initial and final points for measurement.
- When the direction is not considered both are equal in magnitude, in most cases.
- The dimensional formula for Distance and Displacement is the same. i.e [M⁰L¹T⁰]