Distance and displacement are standard measures used regularly in Physics but are also commonly confused ones. Understanding them and their purpose in any scale of measurement is an important step in familiarizing yourself with the core concepts of Physics. 

While at first glance the two names seem to have little to no distinction between them, an in-depth look will help you explore the essential differences between the two.

What Is Distance?

The total measure of the path that an object follows while travelling from one point to another within a certain time is called distance. This may be a direct path or an indirect path between the initial point of the object and its final point.               

What Is Displacement?

Displacement measures the shortest path between the initial point of the object and its final point. This measure disregards the path taken by the object, instead considers the straight-lined path from its initial position to its final position. 

Displacement is also lesser than or equal to distance and never greater.

What are the Differences Between Distance and Displacement?

Some of the main distance versus displacement distinctions are outlined in the following points. These will help you thoroughly understand the concepts of distance and displacement and how they are utilised in calculations in Physics. 

Quantity and direction

Distance is a scalar quantity. As such, it only has a quantity or magnitude and no direction.

Displacement is a vector quantity. Both the direction and the quantity are important for this measure.

Values

The value of distance measured will always be positive.

Displacement, on the other hand, can be zero, positive, or even negative.

Route

Distance considers the route or path the object follows and takes the total sum of the length travelled by the object.

Displacement does take the complete path into account, instead only considers the shortest path between the initial and final point of the object.

Nature of the path

Distance can be measured along a path that is not straight.

Displacement is always measured along a straight path.

Denotation

Distance is denoted by the letter ‘d’.

Displacement is denoted by the letter ‘s’.

Indication

Distance is not indicated with an arrow along the route.

Displacement is indicated with an arrow along the path every time.

Expression Used

Distance is expressed using a number.

Displacement is expressed using a module, unity, and directional arrow.

Some Similarities Between Distance and Displacement

Along with the many differences, distance and displacement also have certain factors that are common between the two. Here are some that you can keep in mind:

Distance and displacement both need a point of reference for their measurement calculation.

Meter (m) is the SI unit of both distance and displacement.

In both cases, the dimension is the same.

If an object moves in a straight line in the same direction, then distance and displacement will be equal.

Mathematical Representation of Distance and Displacement

Formula for distance:

Distance is the total sum of all the paths travelled by the object from one point to another within a certain time. It is mathematically represented as a product of the speed at which the object is moving, and the time it takes for it to travel the distance. 

Distance = Speed x Time

Formula for displacement:

As we’ve seen, displacement is the measurement of the shortest path between the initial point and final point of an object. It is mathematically represented as the product of the rate of change of its position or velocity and the time.

Displacement = Velocity x Time

Why Is the Distinction Important?

If you’re travelling to a particular destination, for example, to your class, you may have to take multiple lefts and rights on the route or take a curved road leading to your class. If you need to know the exact measure of the route you’re taking, what you’ll need to calculate is the distance, considering all the curves, rights, and lefts.

This proves even more useful when you need to determine the time you would take to get from your home, which is your frame of reference, to your class. If you know the speed you’d be travelling at, the time is easy enough to calculate based on the formula for distance. 

Similarly, if you’ve reached your destination from your initial place within a certain period of time, you could likewise determine the speed at which you were travelling.

Simply put, knowing the distance from your home to your class and the time you have left until class begins, can help you figure out whether you need to walk to class or run!

Displacement, on the other hand, is the net direction of travel. This means that it is the shortest path from your home to the class in a straight line. It does not consider any buildings or obstacles along the straight-line path. 

In the above context, if in a straight line, given a particular direction, your home is 1 km away from your class, even though the distance you’ve travelled is 2 kms, your net displacement from home is still 1 km.

Examples of Distance and Displacement

Imagine you’re running on a circular 200-metre track. When you start from a specific point on the track and run around the track and return to the same point, the distance you have travelled is 200 metres. 

However, your displacement is zero. It is because your initial position and final position are the same.

Another example is your daily travel route. If you leave from home, your fixed frame of reference, to school and return home at the end of the day, your total displacement is zero. 

However, if you want to consider your net displacement from your home to school, you’ll need to measure the distance in a straight line between these two locations.

Conclusion

Distance and displacement have various applications in Physics. While distance is a measurement that we use regularly, displacement comes to use in more advanced fields of Physics, such as kinematics. 

Kinematics is a branch of physics that determine the motion of objects, points, and system without considering the cause of such motion. Understanding the distinctions between distance and displacement thoroughly can help you dive deeper into more advanced concepts of Physics later on.