In the equation x = x₀ + vt, 'x₀' means what?

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In summary, the equation x = x₀ + vt represents rectilinear uniform motion with x₀ being the initial position and vt representing the distance traveled in a given amount of time. The final position, xf, is determined by the starting position x₀ and the distance traveled vt. The plus or minus sign indicates the direction of motion towards either positive or negative infinity.
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Indranil
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In the equation x = x₀ + vt, 'x₀' means what?
 
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  • #2
The subscript "0" pretty much always means the original/starting value.
 
  • #3
russ_watters said:
The subscript "0" pretty much always means the original/starting value.
As I know x denotes 'displacement'. If x = 5 meters east, it means it's final position is 5 meters east but 'x₀' denotes what? is the object stationary in this case?
 
  • #4
Indranil said:
In the equation x = x₀ + vt, 'x₀' means what?

It means the initial position of an object.

Indranil said:
As I know x denotes 'displacement'. If x = 5 meters east, it means it's final position is 5 meters east but 'x₀' denotes what? is the object stationary in this case?

If you write, ##x_0 = 5## then that would mean that the initial position of the object is, in a standard cartesian coordinate system (xy-plane), located at 5 units to the right of the origin.
 
  • #5
Indranil said:
As I know x denotes 'displacement'. If x = 5 meters east, it means it's final position is 5 meters east but 'x₀' denotes what? is the object stationary in this case?
If ##x_0 = 5##, this means that the object in question starts out at 5 units in the positive direction (usually eastwards or to the right) from the origin (where x=0). This is the initial position.

The ##x## value being spit out by the function gives you the final position of the object. This can be any new number.

However ##x## is not the displacement. The displacement would be ##\Delta x##, pronounced Delta ##x##. ##\Delta x## is the difference between ##x_0## and ##x##.
 
  • #6
lekh2003 said:
If ##x_0 = 5##, this means that the object in question starts out at 5 units in the positive direction (usually eastwards or to the right) from the origin (where x=0). This is the initial position.

The ##x## value being spit out by the function gives you the final position of the object. This can be any new number.

However ##x## is not the displacement. The displacement would be ##\Delta x##, pronounced Delta ##x##. ##\Delta x## is the difference between ##x_0## and ##x##.
Ok, then what would be the final position ( x ) from the concept above? what would be the final position value? I knew that the initial position is 0 and the final position is 5. Am I correct? Please explain.
 
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  • #7
Indranil said:
In the equation x = x₀ + vt, 'x₀' means what?
x0 is the position at t = 0: the initial position.
 
  • #8
Doc Al said:
x0 is the position at t = 0: the initial position.
Could you please provide me with a diagram so that I can clear my confusion? it's my humble request.
 
  • #9
Indranil said:
Could you please provide me with a diagram so that I can clear my confusion? it's my humble request.
I'm not sure what sort of diagram you're looking for. The equation ##x = x_0 + vt## applies to constant velocity along a single axis (in this case the x axis). It gives you the final position along that axis after some time "t" passes. The final position depends on where you started (given by x0) and the distance you traveled in that time (given by vt).
 
  • #10
Doc Al said:
I'm not sure what sort of diagram you're looking for. The equation ##x = x_0 + vt## applies to constant velocity along a single axis (in this case the x axis). It gives you the final position along that axis after some time "t" passes. The final position depends on where you started (given by x0) and the distance you traveled in that time (given by vt).
Please provide me with any 'initial and final position' diagram. It would be very useful to me.
 
  • #11
Indranil said:
Please provide me with any 'initial and final position' diagram. It would be very useful to me.
Code:
x axis: -----0--------x0-----------------------xf----
             ^        ^                        ^
             Origin   Start here               End here
 
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  • #12
upload_2018-7-23_13-8-15.png

How about this?
 

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  • #13
Indranil said:
In the equation x = x₀ + vt, 'x₀' means what?

These are the coordinate equations for rectilinear uniform motion. x₀ is the coordinate of the starting point of motion. And plus or minus shows the direction of motion. In one case, when plus, it moves toward plus infinity, and when minus, it moves toward minus infinity.
v- velocit
t-unit of time
 
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  • #14
This thread is 5 years old and the OP is no longer at PhysicsForums. Your post does not add anything to what has been said before.

Thread locked.
 

1. What does 'x₀' represent in the equation x = x₀ + vt?

'x₀' is the initial position, or the starting point, in the equation. It is the value of x at the beginning of the experiment or motion.

2. Why is 'x₀' sometimes referred to as the initial displacement?

The term 'displacement' refers to the change in position, and in this equation, 'x₀' represents the initial position before any displacement occurs. Therefore, it is often referred to as the initial displacement.

3. Can 'x₀' have a negative value in the equation x = x₀ + vt?

Yes, 'x₀' can have a negative value if the initial position is in the negative direction from the reference point. This is often seen in physics problems involving motion in one dimension.

4. How is 'x₀' related to the intercept of the x-axis in a graph of x vs. t?

The intercept of the x-axis in a graph of x vs. t represents the initial position or 'x₀'. This is because at time t = 0, the value of x will be 'x₀' in the equation x = x₀ + vt.

5. Is 'x₀' a constant or a variable in the equation x = x₀ + vt?

'x₀' is a constant in the equation as it represents the initial position, which does not change throughout the experiment or motion. It is not affected by any changes in time or velocity.

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