A stone is thrown vertically upward from the top of a building. Does the stone’s displacement depend on the location of the origin of the coordinate system? Does the stone’s ve-locity depend on the origin? (Assume that the coordinate system is stationary with respect to the building.) Explain.
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Considering the coordinate system to be stationary with respect to the building/earth:
Displacement & Origin:
Displacement is a physical quantity that measures the shift in the position of a particle. The displacement of a particle during a certain period of time is measured by the difference of its position vectors at those two time instants bordering the duration under consideration.
Displacement from time t₁ to time t₂ =
Position vector of particle at t₂ - Position vector of particle at t₁
Now, the individual position vectors in the above equation depend on the choice of the origin of the coordinate system. However, their difference doesn't. So the displacement vector is independent of the coordinate system's origin.
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Velocity and Origin:
The instantaneous velocity of a particle is defined as the velocity at an instant of time, i.e., the derivate of the position vector at the time instant under consideration. The average velocity is defined as the displacement of a particle during a certain period of observation divided by the time period.
Instantaneous Velocity= d(position vector)/dt
Average Velocity= Displacement/Time
In both case, the velocity is measured as a quotient of two quantities, both of which are independent of the origin of the coordinate system. Thus, the velocity of a particle is independent of the choice of origin of the coordinate system.
Displacement & Origin:
Displacement is a physical quantity that measures the shift in the position of a particle. The displacement of a particle during a certain period of time is measured by the difference of its position vectors at those two time instants bordering the duration under consideration.
Displacement from time t₁ to time t₂ =
Position vector of particle at t₂ - Position vector of particle at t₁
Now, the individual position vectors in the above equation depend on the choice of the origin of the coordinate system. However, their difference doesn't. So the displacement vector is independent of the coordinate system's origin.
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Velocity and Origin:
The instantaneous velocity of a particle is defined as the velocity at an instant of time, i.e., the derivate of the position vector at the time instant under consideration. The average velocity is defined as the displacement of a particle during a certain period of observation divided by the time period.
Instantaneous Velocity= d(position vector)/dt
Average Velocity= Displacement/Time
In both case, the velocity is measured as a quotient of two quantities, both of which are independent of the origin of the coordinate system. Thus, the velocity of a particle is independent of the choice of origin of the coordinate system.
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