Calculating Instantaneous Velocity Using Particle Coordinates

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In summary, to find the x-component of the instantaneous velocity at t = 5.00s, you need to differentiate the x equation and plug in 5 for t. This will give you the instantaneous velocity, which is time independent.
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Amel
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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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  • #2
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.
 
  • #3
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.
 

What is instantaneous velocity?

Instantaneous velocity is the velocity of an object at a specific moment in time. It is the rate of change of an object's position with respect to time at a given instant.

How is instantaneous velocity different from average velocity?

Average velocity is the total displacement of an object divided by the total time taken, while instantaneous velocity is the velocity of an object at a specific moment in time. Average velocity provides an overall picture of an object's motion, while instantaneous velocity shows the velocity at a specific point in time.

How is instantaneous velocity calculated?

Instantaneous velocity is calculated by taking the limit of the average velocity as the time interval approaches zero. This is represented by the formula: v = lim Δt→0 (Δx/Δt), where v is the instantaneous velocity, Δx is the change in position, and Δt is the change in time.

What factors can affect instantaneous velocity?

The instantaneous velocity of an object can be affected by factors such as acceleration, direction, and changes in position. Other external factors, such as friction and air resistance, can also impact an object's instantaneous velocity.

Why is instantaneous velocity important in scientific research?

Instantaneous velocity is an important concept in scientific research as it allows us to analyze an object's motion at a specific moment in time. It helps us understand how objects move and interact with their environment, and can aid in the prediction and control of an object's movement.

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