The numerical ratio of displacement to distance for a moving object is: * (a) Always less than 1 (b) Equal to 1 or less than 1 (c) Always more than 1 (d) Equal to 1 or more than one Also give the reason.?

Question

Answer

Equal to one or less than one
Reason -
Distance is the area covered by the object.
Displacement is the shortest distance.
If the road is straight then displacement will be equal to the distance covered but if the path is circular, then the displacement will be 0 as object comes the same place and displacement is the shortest distance covered by the object but distance would be more.

Answer

Equal to less than 1

We know, magnitude of displacement is the staright line distance between the initial point and the final point of the path of the moving body.
Dispalcement could be negative, positive or zero. but distance is always positive or zero when there is no motion.
So, the ratio of displacement to distance for a moving object is equal to less than 1.

Answer

The numerical ratio of displacement to distance for a moving object is always less than 1.

Explanation:

Displacement and Distance:
- Displacement: Displacement refers to the change in position of an object in a particular direction. It is a vector quantity and is represented by an arrow pointing from the initial position to the final position of the object. Displacement takes into account both the magnitude (distance) and the direction of the motion.
- Distance: Distance refers to the total length covered by an object during its motion. It is a scalar quantity and is always positive. Distance only considers the magnitude of the motion and does not take into account the direction.

Numerical Ratio of Displacement to Distance:
- The numerical ratio of displacement to distance is calculated by dividing the displacement of the object by the distance traveled.
- Mathematically, this ratio can be represented as follows: Displacement/Distance.

Always less than 1:
- The numerical ratio of displacement to distance is always less than 1.
- This is because displacement takes into account the shortest path between the initial and final positions of the object, while distance considers the total length covered by the object.
- In most cases, the displacement is shorter than the distance traveled.
- The only scenario where the displacement and distance are equal is when the object moves in a straight line without changing direction.

Example:
- Let's consider an example to illustrate this concept. Suppose an object moves from point A to point B and then returns back to point A. The total distance covered by the object is the sum of the distances from A to B and from B to A.
- However, the displacement of the object is zero because it ends up at the same position where it started.
- In this case, the numerical ratio of displacement to distance is 0/2d, where d represents the distance between points A and B. This ratio is equal to 0, which is less than 1.

Conclusion:
- The numerical ratio of displacement to distance for a moving object is always less than 1, except in the case where the object moves in a straight line without changing direction.
- Displacement takes into account both the magnitude and direction of the motion, while distance only considers the magnitude.
- It is important to understand the difference between displacement and distance when analyzing the motion of objects.

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