Finding Velocity and Position of a Moving Particle: A Function of Time

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Homework Help Overview

The problem involves a particle moving along the x-axis with constant velocity, requiring the determination of the particle's velocity and the formulation of an equation that relates position to time.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the calculation of velocity and the formulation of a linear equation for position as a function of time. There is questioning of assumptions made in the initial calculations and attempts to clarify the relationship between distance, time, and velocity.

Discussion Status

Some participants have provided guidance on correcting earlier mistakes and have explored the implications of the linear relationship between position and time. There is an ongoing exploration of the correct formulation of the equation.

Contextual Notes

There is a focus on ensuring the correct application of the concept of constant velocity and the interpretation of the initial conditions provided in the problem statement.

Loppyfoot
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Homework Statement


A particle moving along an x-axis with constant velocity is at the point x=1 when t=2 and is at the point x=5 when t=4. Find the velocity of the particle if x is in meters and t is in seconds. Find an equation that expresses x as a function of t.


Homework Equations





The Attempt at a Solution


I got the first part. (4-2)/(5-1) = 0.5m/s. Now, how do I get the equation that expresses x as a function of t?
 
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You got the first part by assuming that the object covers equal distances in equal times. Can you write an equation that expresses that?

** Edit **

Actually you did not get the first part. You divided time interval by displacement.
 
Last edited:
Oh, so would the velocity be 2?
Ok, so x=2t+?
So, it is 2t-3.
Right?
 
Last edited:
Yes, x is directly proportional to time, the constant of proportionality being the velocity. To find the velocity, you need to do part (a) correctly. The y intercept in this case is the position of the particle at time t = 0.
 
So when time = 0, the particle is at coordinate x=-3.
 
You got it.
 
Thanks for notifying me of my mistake!
 

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