Calculating Instantaneous Velocity Using Particle Coordinates

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To calculate the x-component of instantaneous velocity for a particle defined by its coordinates, one must differentiate the x-coordinate equation with respect to time. Plugging in the time value directly provides the position, not the velocity. The differentiation reveals that the instantaneous x-velocity is independent of time. This realization clarifies the problem as a trick question, emphasizing the importance of understanding derivatives in physics. The correct approach confirms that the instantaneous velocity can be determined without needing to substitute specific time values.
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Homework Statement



The location of a particle (in m) is given by its x, y and z coordinates as function of the time (in s) as:

x = -33+29t and y = -11-27t+7t2 and z = 95-9t-5t2

Calculate the x-component of the instantaneous velocity at t = 5.00s.



Homework Equations





The Attempt at a Solution



Ok so I thought you just plug 5 into t for the x = equation but I guess not. How do I figure this out?
 
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Plugging 5 for t in the X equation will give you the X-position of the particle at t=5s.

This is kind of a trick question, tbh. Differentiate the x equation, this will give you instantaneous X-velocity as a function of time. You'll see that it is time independent.
 
Cool thanks, the first time that's what I did but I must have entered it wrong because got it right this time.

Thanks, and yeah I see that t doesen't matter.
 
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