Q: What is the distance between an object and its reference point?

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If the reference point and an object are both on the horizon then the angular distance to the object, relative to the reference point is simply the angle formed between the two rays from the observer to object and to the reference point. If either the object or reference point (or both) are not in the plane of the horizon then the appropriate rays are the projections of the rays from the observer onto the plane containing the horizon.

The vertical axis gives the distance of an object from a fixed point - the point of reference - after a time, as measured on the horizontal axis.

The object is at some reference point at time b. The object moves at a constant speed (in a radial direction). Its speed is 1/a units of distance per each unit of time. Equivalently, it takes a units of time to move a unit of distance. The formula gives the time taken to get to a distance of x units from the reference point.

It shows the speed of an object in a direction towards or away from the reference point. This is not the speed of the object because any motion in a transverse direction is ignored. For example, even if a racing car is going at top speed around the reference point on a circular track, the distance v time graph will be a horizontal line. The slope will be zero.

A distance-time graph shows the movement of an object with respect to time. The average slope between any two points on the graph is equal to the average velocity of the object between those two points. The instantaneous slope (or derivative) at a point on the graph is equal to the instantaneous velocity of the object at that point.

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That can't be told. You would have to measure that or figure it out yourself. There is no way anyone can give you an actual answer.

An object is in motion only if its distance from a reference point is changing. The average speed of the object is given by the object's rate of change of displacement from the reference point over time.

If the reference point and an object are both on the horizon then the angular distance to the object, relative to the reference point is simply the angle formed between the two rays from the observer to object and to the reference point. If either the object or reference point (or both) are not in the plane of the horizon then the appropriate rays are the projections of the rays from the observer onto the plane containing the horizon.

A reference point is part of the definition of movement or displacement. The difference, over time, of your distance or orientation to a given reference point or points defines movement.

A reference point is part of the definition of movement or displacement. The difference, over time, of your distance or orientation to a given reference point or points defines movement.

The vertical axis gives the distance of an object from a fixed point - the point of reference - after a time, as measured on the horizontal axis.

One needs the direction.

Deciding if an object is moving isn't as easy as it sounds. We can only discern relative motion and we have to use reference points. (A reference point is an object that is not moving that you compare to the other object.) An object is in motion when it's distance from the reference point is changing.For example, you could say that you and this computer are not moving. Other than your eyes blinking, chest pumping up and down, and you clicking on the mouse, you and this computer are not in motion. Since the distance between you and the computer is not changing, you can conclude that neither you or the computer are moving.

I believe you find that an object is in motion if the distance between it and a reference point is changing. A reference point is another object that is not moving that you would use to calculate if an object is moving.

Yes, that is one meaning of "reference point", although the reference point need not be an object, but may simply be a location.

No because enable to see if the object is moving it needs a reference point other than itself.

To support you in specifying how the reference point is placed and how the object is moved away from the reference point.