Difficulty with a basic motion problem

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Homework Help Overview

The problem involves calculating average and instantaneous velocities and accelerations for an object whose position is defined by a polynomial function of time. The context is within the subject area of kinematics.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the formulas for average velocity and average acceleration, with some clarifying the relationship between position, velocity, and acceleration through derivatives. The original poster expresses uncertainty about how to apply these concepts to find the required velocities for average acceleration.

Discussion Status

There is an ongoing exploration of the necessary formulas and their application. Some participants have provided clarifications regarding the definitions of average velocity and acceleration, while the original poster is seeking further guidance on the calculations.

Contextual Notes

The original poster has successfully solved part of the problem but is struggling with the next steps. There may be assumptions regarding the understanding of derivatives and their application in this context.

frankfjf
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This time I'm having trouble with this problem:

If the position of an object is given by x = 2.30t^5, where x is measured in meters and t in seconds, find (a) the average velocity and (b) the average acceleration between t = 1.0 s and t = 2.0 s. Then find (c) the instantaneous velocity v and (d) the instantaneous acceleration a at t = 1.0 s. Next find (e) v and (f) a at t = 2.0 s.

I have solved a, but am uncertain how to obtain the two velocities needed for b according to the formula for average velocity. What do I need to do?
 
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the velocity function is the time-derivative of the location function.

the acceleration function is the time-derivative of the velocity function.
 
the average velocity forumula is [f(b)-f(a)]/b-a, the avg. acceleration formula is essentially the same except that for the values of f(b) and f(a) you need to take the derrivative of the position equation to give the velocity values
 
aud11888 means that average velocity = [tex]\frac{x(t_b) - x(t_a)} {t_b - t_a}[/tex]
 

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