Particle problem, velocity and acceleration

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Homework Help Overview

The problem involves a particle moving along the x-axis, with its position defined by a polynomial equation in terms of time. Participants are tasked with finding displacement, velocity, and acceleration over specified time intervals.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the need to differentiate the position function to find velocity and acceleration. There are questions about how to handle the time intervals for velocity and acceleration calculations beyond the initial displacement.

Discussion Status

Some participants have provided guidance on using derivatives to find the necessary quantities, while others express uncertainty about their understanding of the calculus concepts involved. There is a mix of attempts to clarify the problem and share personal learning experiences.

Contextual Notes

One participant notes a lack of foundational knowledge in calculus, which may affect their ability to engage with the problem fully. The original poster indicates confusion regarding the time intervals specified in the problem.

tigerlili
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Homework Statement



The position of a particle moving along the x-axis depends on the time according to the equation x = ct4 - bt8, where x is in meters and t in seconds. Let c and b have numerical values 2.4 m/s4 and 1.9 m/s8, respectively. From t = 0.0 s to t = 1.3 s, (a) what is the displacement of the particle? Find its velocity at times (b) 1.0 s, (c) 2.0 s, (d) 3.0 s, and (e) 4.0 s. Find its acceleration at (f) 1.0 s, (g) 2.0 s, (h) 3.0 s, and (i) 4.0 s.

Homework Equations



x = ct4 - bt8

v= disp/time

v=vo + at

The Attempt at a Solution



i got part a correct, i know the displacement is -8.64 meters
what I'm really having trouble with.. is the idea that the problem clearly states that the time interval is 0 to 1.3 seconds.. and then it asks you to find velocity and acceleration for up to 4 seconds. how is this done? i know that you can't just do v= disp/time using -8.64 meters/1 second for part b, because it said the answer was wrong. please help?
 
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This problem requires using calculus to take the derivative of x.
 
is there any possible way that you could explain further?
 
is it just.. that i take the first derivative of the function to find the velocities, and the 2nd derivative to find the acceleration?
 
tigerlili said:
is it just.. that i take the first derivative of the function to find the velocities, and the 2nd derivative to find the acceleration?

Yes, exactly. Has that been covered in your class yet?
 
honestly.. no. we've had 3 classes and I've learned absolutely nothing, other than the fact that my teacher knows how to throw a beanie baby up in the air...
 
thank you very much for your help- i finally got the whole problem!
 

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