The distance and the displacement are measured in meters/miles and talk about the total length covered by an object. In this article, let us discuss is distance and displacement same or not.
The distance is scalar property because it measures the total distance laps by the object. On the contrary, the displacement is a vector quantity, and it measures not only the distance but also the direction of the displacement of a body from its initial position.
When distance and displacement are same?
The distance and displacement can be the same when the object travels in a straight line or does not move in the reverse direction.
If the object moves just in one direction along the straight path, then the total distance covered by an object and the total displacement of an object remains the same. If a boy climbs the inclined path to reach the top of the hill, his total displacement and the distance covered will be the same.
Let us say that the distance from the plane ground to the top of the hill is ‘d’ m. The boy covers ‘d’ m to reach the top of the hill, and the total displacement and distance covered at this time is ‘d’ m.
Now, if he climbs down the hill and reaches the plane ground, his total displacement will become zero because the change in his initial and final position has become zero, and the total displacement now is d + d = 2d.
How distance and displacement are same?
The distance and displacement both measures the total length/miles covered. The units of measuring both the quantities are also the same.
The distance covered by the object in motion can be equal to the total displacement of that object if it is moving in a straight path with taking the reverse path of motion or a turn. If the object takes a turn, then the total displacement of the object becomes the shortest distance connecting its initial and final position.
The major difference between the distance and the displacement is that the displacement is a vector quantity, and based on that, we can take the displacement quantity as negative. Well, the distance cannot be negative.
The displacement is a vector quantity; therefore, it considers the direction of propagation of an object and the net displacement of a body from its initial position with time, irrespective of the total distance covered by an object.
Why distance and displacement are same?
The distance and displacement both are the same because both determine the total path traveled by the object.
It is also true that the total path length covered by a subject is equal to the displacement and as well as the distance if it has moved along in a straight line. This is achieved when there are no variations in the direction in which the object travels.
The distance cannot be equal to the displacement because it is the total distance the object has covered along the path.
If the object is moving with a particular speed that is known, then its distance covered can be measured at any time using the following formula:-
Distance = Speed × Time
d (m) = s (m/s) × t (sec)
and the displacement is measured as,
Displacement = Velocity × Time
d (m) = v (m/s) × t (sec)
The units for measurement for both properties are the same. The only difference is that the distance is proportional to the speed of an object, which is a scalar and the displacement depends upon the vector product of the velocity, which has a direction too.
When distance and displacement are different?
If the path in which the object travels is not straight, then the distance and the displacement of an object are different.
The distance is the total length covered. On the contrary, the displacement is a net distance between the line connecting the initial and final coordinates of position. The distance and displacement for the same object will differ if the direction of motion changes.
The distance is measured as the product of the speed of an object and the time taken to cover a particular distance. In comparison, displacement is the product of the velocity of an object propagating in a given direction and the time taken for a displacement.
Relation between Distance and Displacement
The distance and displacement both measures the total path length traveled by the object and are measured in meter/miles/km. The distance covered by the object will keep on adding, but the net displacement of an object varies continuously if the direction of motion of an object varies.
Explain the Relation between Distance and Displacement with an Example
Consider a boomerang. When a boomerang is released from the hand, giving it torque, it travels to a certain distance, ‘x’. Until the boomerang travels to the distance ‘x’, the distance and the displacement for the boomerang are the same. But, after covering the distance ‘x’, it turns and returns towards the side from where it was thrown.
Upon reaching the boomerang in the hands of the thrower, the displacement becomes zero. Because the boomerang travels in the reverse direction, that is, in the negative axis. Thus the distance travelled along this path is ‘-x’. Hence, the total displacement of a boomerang becomes x + (-x) = x – x = 0. But the total distance covered by the boomerang is x + x = 2x.
Hence, the displacement of an object depends upon the direction of motion of an object, while the distance does not depend upon the direction of motion.
Difference between Distance and Displacement
The distance is a scalar quantity and defines only the magnitude of the speed. While the displacement depends upon the direction of speed.
The distance is always positive because it measures only the magnitude, while the displacement can be negative, positive, and zero, depending on the direction of propagation. The total distance is the sum of all the path lengths an object covers, while the net displacement between the two points is the length of the line connecting both points.
A person practicing with reverse gear takes the car in the reverse direction for 300m, then drives in a forward direction for 450m, then again takes the car in the reverse direction for 400m and moves the car forward for 300m. What is the total distance and displacement of a car?
Given:- The distance covered in a reverse direction for a = 300m.
The distance covered in the forward direction is b = 450m.
The distance covered in the reverse direction is c = 400m.
The distance covered in the forward direction is d = 300m.
The distance traveled while driving is,
Distance = a + b + c + d = 300m + 450m + 400m + 300m = 1450m
Therefore, the total distance covered by the car is 1450m.
The displacement in the forward direction will be positive, while the displacement in the negative direction will be negative.
Hence, we get,
Displacement = a – b + c – d = 300m – 450m + 400m – 300m = -50m.
Hence, the net displacement of a car is -50m. This implies that the driver drove the car 50m extra in the reverse direction.
The values of both, distance and displacement, will vary for an object in motion if its direction of mobility varies. Hence, the displacement and distance covered by an object will vary if the direction of motion of an object changes.