Difference Between Distance and Displacement
The concepts of distance and displacement are considered crucial in motion in the study of physics. In everyday discussions, most of the time, distance and displacement appear in one category, but in science, these words differ from each other. The main difference between them is that distance is a scalar quantity or a measure of total path that has been covered by an object; whereas, displacement is a vector quantity, which is defined as the length of the shortest path to "follow" direction between the starting and the ending point.
This Story also Contains
- What is Distance
- What is Displacement
- Difference between Distance and Displacement
These concepts are not only important for higher class but also crucial for school learning. Be it exams to prepare for like JEE Main or NEET or even boards like CBSE, ICSE, and even state level such as Maharashtra Board, knowing distance and displacement goes a long way in falling in kinematics, which is actually an opening chapter in physics, functional in preparing a learner for serious battling in competition. There are many versions of this topic in both school and entrance tests, so understanding the definitions and examples of real-life applications is crucial.
What is Distance
- The length of the path traversed is called path length or distance.
- Consider the motion of a car along a straight line. We choose the x-axis such that it coincides with the path of the car’s motion and the origin of the axis as the point from where the car started moving, i.e. the car was at x = 0 at t = 0.
- Let P, Q and R represent the positions of the car at different instants of time.
- Consider two cases of motion.
- In the first case, the car moves from O to P. Then the distance moved by the car is OP = +360 m. This distance is called the path length traversed by the car.
- In the second case, the car moves from O to P and then moves back from P to Q. During this course of motion, the path length traversed is OP + PQ = + 360 m + (+120 m) = + 480 m.
- The distance is a scalar quantity — a quantity that has a magnitude only and no direction
- SI unit of Distance: m
- Dimension of Distance: [Pathlength]=[L]
What is Displacement
- Let $x_1$ and $x_2$ be the positions of an object at time $t_1$ and $t_2$. Then its displacement, denoted by $\Delta x$, in time $\Delta t=\left(t_2-t_1\right)$, is given by the difference between the final and initial positions : $\Delta x=x_2-x_1$ (We use the Greek letter delta ( $\Delta$ ) to denote a change in a quantity.) If $x_2>x_1, \Delta x$ is positive; and if $x_2<x_1, \Delta x$ is negative.
- Displacement has both magnitude and direction. Such quantities are represented by vectors. You will read about vectors in the Mathematical tools for physics chapter.
- Presently, we are dealing with motion along a straight line (also called a rectilinear motion) only.
- In one-dimensional motion, there are only two directions (backwards and forward, upward and downward) in which an object can move, and these two directions can easily be specified by + and - signs. For example, the displacement of the car moving from $O$ to $P$ is :
$
\Delta x=x_2-x_1=(+360 \mathrm{~m})-0 \mathrm{~m}=+360 \mathrm{~m}
$
- The displacement has a magnitude of 360 m and is directed in the positive x direction as indicated by the + sign. Similarly, the displacement of the car from P to Q is 240 m-360 m=-120m. The negative sign indicates the direction of displacement. Thus, it is not necessary to use vector notation for discussing the motion of objects in one dimension.
- The magnitude of displacement may or may not be equal to the path length (distance) traversed by an object or in other words, the distance travelled is always greater than or equal to the magnitude of displacement.
Distance $\geq \mid$ Displacement $\mid$
For example, for the motion of the car from O to P, the path length is +360 m and the displacement is +360 m. In this case, the magnitude of displacement (360 m) is equal to the path length (360 m). But consider the motion of the car from O to P and back to Q. In this case, the path length = (+360 m) + (+120 m) = + 480 m. However, the displacement = (+240 m) – (0 m) = + 240 m. Thus, the magnitude of displacement (240 m) is not equal to the path length (480 m).
- The magnitude of the displacement for a course of motion may be zero but the corresponding path length is not zero.
- For example, if the car starts from O, goes to P and then returns to O, the final position coincides with the initial position and the displacement is zero. However, the path length of this journey is OP + PO = 360 m + 360 m = 720 m.
- SI unit of Displacement: m
- Dimension of Displacement: [Displacement]=[L]
Points to ponder:
- The displacement depends only on the endpoints; the path length (as the name implies) depends on the actual path.
- In one dimension, the two quantities are equal only if the object does not change its direction during the course of motion.
- In all other cases, the path length is greater than the magnitude of displacement
- The magnitude of the displacement for a course of motion may be zero but the corresponding path length is not zero.
Key points to remember:
- The coordinate system along with a clock constitutes a frame of reference.
- If one or more coordinates of an object change with time, we say that the object is in motion
- The description of an event depends on the frame of reference chosen for the description.
- The magnitude of displacement may or may not be equal to the path length (distance) traversed by an object or in other words, the distance travelled is always greater than or equal to the magnitude of displacement.
Distance $\geq \mid$ Displacement $\mid$
- If an object moving along a straight line covers equal distances in equal intervals of time, it is said to be in uniform motion along a straight line.
Difference between Distance and Displacement
The difference between distance and displacement is given in the table.
| Sl. No. | Different properties | Distance | Distance |
| 1. | Definition | The distance between any two points is the total length of the path. | The direct length between any two points measured along the shortest path between them is called displacement. |
| 2. | Denotation | d | s |
| 3. | Direction Consideration | The direction is ignored when calculating distance. | The direction is taken into account when calculating displacement. |
| 4. | Quantity | The magnitude, not the direction, determines the value of a scalar quantity. | Because it depends on both magnitude and direction, displacement is a vector quantity. |
| 5. | Route Information | The term "distance" refers to the specific route information used when travelling from one location to another. | Because displacement only refers to the quickest way, it does not provide entire route information. |
| 6. | Formula | speed × time | velocity ×time |
| 7. | Possible values | Only positive numbers can be used in the distance. | Positive, negative, or even zero displacement is possible. |
| 8. | Measurement in non- non-straight path | A non-straight path can be used to calculate the distance. | Only a straight road may be used to quantify displacement. |
| 9. | Indication | An arrow does not represent distance. | An arrow is always used to denote displacement. |
| 10. | Path dependence | The distance is determined by the path followed, and it varies depending on the way taken. | Displacement is independent of the path and solely depends on the body's initial and ending positions. |
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Frequently Asked Questions (FAQs)
Power is calculated using velocity rather than speed because it represents the rate of energy transfer, which depends on how quickly displacement occurs in the direction of the force, not just how fast something is moving. This is why you can expend a lot of energy (high power) pushing against a wall without actually moving it (zero speed but non-zero velocity of attempt).
Yes, consider a runner on a circular track who completes exactly one lap, returning to the starting point. The average speed is non-zero (distance traveled divided by time), but the average velocity is zero because the displacement is zero (start and end points are the same).
Acceleration is more directly related to displacement than distance. It's defined as the rate of change of velocity, which itself is the rate of change of displacement. While distance can increase steadily (like in uniform circular motion), acceleration depends on how displacement changes over time, including changes in direction.
You can have both distance-time and displacement-time graphs for circular motion, but they look very different. A distance-time graph for circular motion is a straight line (distance increases steadily). A displacement-time graph is more complex - it's periodic, often sinusoidal, as displacement oscillates between zero and the diameter of the circle.
As a path becomes more complex (with more turns, loops, or deviations), the difference between distance and displacement generally increases. In a straight line, they're equal. In a slightly curved path, distance is a bit larger than displacement. In a very complex path (like a scribble), distance can be much larger than displacement. The ratio of displacement to distance can be seen as a measure of the path's "directness".
In animal migration, both distance and displacement are important. The total distance traveled gives information about the energy expended and the endurance required for the journey. The displacement indicates the net change in location and can help in understanding navigation methods, the influence of geographical features, and the efficiency of the migration route.
In quantum mechanics, the concepts are applied differently. The distance a particle travels isn't always well-defined due to the uncertainty principle. However, displacement remains a useful concept, particularly in understanding wave functions and probability distributions of particle positions. The displacement of an electron in an atom, for instance, is crucial in determining its energy levels.
Work is defined as the product of force and displacement (in the direction of the force) because it represents the energy transferred when a force moves an object. This transfer depends on the net change in position (displacement), not the total path length (distance). Using displacement ensures that no work is done when an object returns to its starting point, conserving energy in closed systems.
Momentum conservation is more directly related to displacement than distance. In a closed system, the total momentum before and after a collision is conserved, regardless of the distances individual objects travel. The displacements of the objects are what determine their final velocities and thus their final momenta.
In special relativity, the distinction becomes even more important. The proper distance (similar to displacement) between two events in spacetime is invariant for all observers, while the distance traveled can vary depending on the observer's frame of reference. This leads to effects like length contraction, where the measured distance between two points can change for objects moving at high speeds.
