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Home > News & Articles > Difference Between Distance and Displacement: Definitions, Examples, Formulas, Properties, and Sample Questions
Updated on 26th October, 2023 , 6 min read
The distinction between distance and displacement is one of the most frequently questioned and perplexing problems in the field of physics. The major difference between distance and displacement is that distance is the length of a path between two points, while displacement is the shortest distance between two points. Although distance and displacement seem similar, they are different quantities with different meanings and definitions.
Distance is defined as the complete route traveled by a body while in motion. The distance may alternatively be defined as the actual length of a body's route from one location to another. Because it is a scalar quantity, there is no need to consider the direction of its motion when calculating distance. The meter is the SI unit of distance. It is also symbolized by the letter "d." There is no need to denote it with an arrow just because it is a scalar quantity. The graphic below provides a better understanding-
Displacement is sometimes defined as the shortest length of a path traveled by a body from one location to another. Simply put, it shows us how far a body has moved from its original location. And, because it is a vector quantity, the direction of motion must be considered when calculating displacement. The meter is the SI unit of displacement. It is also indicated by "s". Because displacement is a vector quantity, it is always denoted by an arrow.
An object's distance can be defined as the object's whole path traversed. As an example. If a car goes east for 5 kilometers before turning north for another 8 kilometers, the total distance covered by an automobile is 13 kilometers.
If an object moves relative to a reference frame, such as a professor moving to the right of a whiteboard or a passenger moving toward the back of an airplane, the item's location changes. This shift in location is referred to as "displacement."
Note: As a result of our examples of distance and displacement, we may conclude that distance has only one magnitude, independent of direction. However, displacement considers both the magnitude and direction of an object's journey. As a result, distance is a scalar number, but displacement is a vector quantity. Displacement can be positive, negative, or zero, but distance is always positive or zero.
Distance can be defined mathematically as,
Distance is the sum of all pathways traveled to go from one location to another.
Speed = Distance / Time
Displacement can be defined mathematically as,
Velocity = Displacement / Time
Therefore,
Distance may have several qualities. Some of them are as follows-
There are several displacement qualities. Some of them are as follows-
Triangle Law of Vector Addition
The following table compares distance and displacement-
Particulars | Distance | Displacement |
Definition | It is the total length of the path between any two places. | It is defined as the direct distance between any two places measured via the shortest path between them. |
Symbol | d | s |
What is it? | The whole length of the avenue traveled by the body. | The shortest distance between the beginning and terminating points. |
Formula | Speed x Time | Velocity x Time |
Example | If an automobile goes east for 5 kilometers before turning west for another 15 kilometers, the total distance covered is 20 kilometers. | If an automobile goes east for 5 kilometers before turning west for another 15. The displacement will equal the length of the line connecting the two points. |
Consideration for Direction | The direction is ignored while calculating distance. | The direction is taken into account while calculating displacement. |
Route Information | Distance provides thorough route information for traveling from one location to another. | Because displacement refers to the quickest way, it does not provide complete route information. |
Quantity | It is a scalar number since it is determined solely by magnitude and not by direction. | It is a vector quantity since it is affected by both magnitude and direction. |
Path Dependence | Distance is path dependent, meaning it varies depending on the path followed. | It is independent of the route and is determined only by the beginning and ending positions of the body. |
Effect on Time | Distance constantly grows farther with time. | The displacement reduces with time. |
Possible Values | Only positive numbers can be assigned to the distance. | Displacement can be positive, negative, or even 0 in some cases. |
Indication | An arrow does not represent distance. | An arrow is usually used to denote it. |
Measurement in a Non-Straight Path |
A non-straight path can be used to calculate the distance. |
Only a straight road may be used to quantify displacement. |
Solution: Displacement is the right answer because only displacement can be zero after some time in this instance.
Solution: A train carriage is quite small in comparison to the distance between the two stations. As a result, the carriage may be thought of as a point-sized object, and a monkey's size is small in comparison to the size of a circular track. As a result, the monkey may be thought of as a point-sized item on the track.
Solution: As the particle's distance traveled is zero. This means that the particle is motionless or at rest. As a result, its displacement is similarly zero.
Solution: Displacement = 0
Therefore,
Distance = 2.5 km + 2.5 km = 5 km.
Solution: If the distance traveled by a body equals the displacement, then the magnitude of an object's average velocity equals its average speed.
Solution: Rectangular circumference = 2 x (100 meters + 50 meters) = 300 meters.
A runner travels twice around a rectangle = 2 x (300 meters) = 600 meters.
Therefore, the distance traveled by the runner is 600 m and the displacement is 0.
Solution: Distance is defined as a body's actual route traveled, whereas displacement is the distance between the beginning and end places. As a result, if a body is displaced by some quantity, it must travel some distance.
Solution: Total distance traveled by the athlete = 3 x track circumference
Distance = 3 x 2 x 30 meters
= 565.2 meters
The displacement is 0 since the athlete returns to the same position A after three cycles.
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By - Nikita Parmar 2023-08-25 09:48:44 , 11 min readAns. The pace at which an item moves along a route in time is defined as speed, whereas velocity is the rate and direction of movement. In other words, speed is a scalar value, but velocity is a vector.
Ans. If the distance traveled is 0, the body was at rest the whole time; hence, displacement is zero since the beginning and end positions coincide.
Ans. As the particle’s distance traveled is zero. This means that the particle is motionless or at rest. As a result, its displacement is similarly zero.
Ans. According to Newton’s third rule, every action has an equal and opposite response. As a result, if object A exerts a force on item B, object B will exert an equal but opposite force on object A.
Ans. Velocity is a vector quantity. The velocity of an object is its speed in a certain direction.
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