Understanding Mean Position

What is the definition of a mean position?

In mathematics, the term “mean” has a specific meaning (i.e., the arithmetical mean is the sum of a set of numbers divided by the size of the set). A medium position is any position in the middle of two other extreme situations. It is defined as a stance in the middle of the road or a compromise between two opposing viewpoints.

What is an object’s position?

Any object’s True Position is its exact coordinate or location as defined by its basic dimensions or other means. Let’s find out What is Position?

Position refers to how far a feature’s location can deviate from its “True Position”.

The trajectory of a rectilinear movement is that of a straight line. This movement is also carried out at a constant rate of acceleration. On a straight line, the origin may be x=0, with an observer measuring the position x of the moving object at time t.

As a result, the mobile’s position x can be connected to time t using the polynomial function below.

position = initial position + (initial velocity×time)+ ½×acceleration×(time)2.

When anything moves from one position to another, it is referred to as displacement. Assume that you’re transferring a ball from point x1 to point x2.

The formula for the Position:

The position change Δx(position formula) is determined as,

Δx=x2–x1

Where,

X2= First Position

X1 = Second Position

Δx = Change of Displacement

If the body changes its position after some time t, then the change in position at any time t will be represented as x(t). Its formula is:

x(t) = ½ at2+v0t+x0

Where,

X(t) – Position of the body concerning time t

X0 – the initial position of the body

V0 – the initial velocity of the body

a – acceleration of the body possesses

position = initial position+initial velocity×time+1/2×acceleration×(time)2

Thus, something travels from one point to another; it is called displacement. Assuming the moving a ball from position x1 to position x2.

What does the slope represent on a position graph?

The slope of a position graph represents the velocity of the object. So the value of the slope at a particular time represents the object’s velocity at that instant.

Another thing to remember is that the slope of a position graph determines the instantaneous velocity at a given point in time. You may get the average velocity between two places in time by calculating the average slope between them. The average velocity does not have to match the instantaneous velocity. If, on the other hand, the slope remains constant over time (i.e., the graph is a straight line segment), the instantaneous velocity equals the average velocity between any two places on the line segment.

What does a location graph’s curvature indicate?

When the slope of a location graph changes, the velocity changes. Acceleration occurs when velocity changes. Curvature on a graph indicates that the object is speeding up and changing its slope.

On a position graph, what does the vertical axis represent?

The object’s position is represented via the vertical axis. Time is represented via the horizontal axis. 

To summarize, if the curvature of the position graph looks like an upside-down bowl, the acceleration will be negative. If the curvature looks like a right side up bowl, the acceleration will be positive. Here’s a way to remember it: if your bowl is upside down, all your food will fall out, which is negative. If your bowl is right side up, all your food will stay in it, which is positive.

Solved Example

Q: A boy who has an initial velocity of 3ms−1 moves for a distance of 20 m. If it’s, the angular acceleration is 2ms−2. Determine the position of the boy at the end of 5 sec.

Solution:

Known parameters:

V0  (Initial velocity)  = 3ms−1,

X0  (distance)  = 20 m,

a (angular acceleration)  = 2ms−2,

t (time) = 5s

The alteration in the position of the boy at instant of time t may be computed as:

X(t) = 1/2at2+v0t+X0

Thus,

X(6) = 0.5×2×52+3×5+20

= 25m + 15m + 20 m

= 60 m.

The boy’s position at the end of 5 sec will be 60 meters.

Conclusion :

Any object’s True Position is its exact coordinate or location as defined by its basic dimensions or other means. Put another way; position refers to how far a feature’s location can deviate from its “True Position.”The trajectory of a rectilinear movement is that of a straight line. This movement is also carried out at a constant rate of acceleration. On a straight line, the origin may be x0, with an observer measuring the position x of the moving object at time t. As a result, the mobile’s position x can be connected to time t using the polynomial function below.

 x(t) = ½ at2+v0t+x0