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Indranil
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In the equation x = x₀ + vt, 'x₀' means what?
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?russ_watters said:The subscript "0" pretty much always means the original/starting value.
Indranil said:In the equation x = x₀ + vt, 'x₀' means what?
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.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?
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.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##.
x0 is the position at t = 0: the initial position.Indranil said:In the equation x = x₀ + vt, 'x₀' means what?
Could you please provide me with a diagram so that I can clear my confusion? it's my humble request.Doc Al said:x0 is the position at t = 0: the initial position.
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).Indranil said:Could you please provide me with a diagram so that I can clear my confusion? it's my humble request.
Please provide me with any 'initial and final position' diagram. It would be very useful to me.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).
Indranil said:Please provide me with any 'initial and final position' diagram. It would be very useful to me.
x axis: -----0--------x0-----------------------xf----
^ ^ ^
Origin Start here End here
Indranil said:In the equation x = x₀ + vt, 'x₀' means what?
'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.
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.
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.
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.
'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.