When can instantaneous velocity equal average velocity during a 10-second trip?

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Homework Help Overview

The problem involves determining when the instantaneous velocity of a particle, described by the position function s(t) = 3t² - 3t + 5 cm, equals the average velocity over a 10-second interval.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the calculation of instantaneous velocity using the derivative of the position function and express uncertainty about how to compute the average velocity for the trip.

Discussion Status

Some participants have provided calculations for instantaneous velocity but are seeking clarification on how to find the average velocity. There is an ongoing exploration of definitions and methods related to both types of velocity.

Contextual Notes

Participants have noted the importance of not cross-posting in different forums, which may lead to confusion in responses. There is an emphasis on providing attempts to solve the problem as part of the discussion.

sammiyahc0
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The position of a particle moving in a straight line during a 10–second trip is s(t) = 3t2 − 3t + 5 cm.Find a time t at which the instantaneous velocity is equal to the average velocity for the entire trip
 
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Show us some attempt at least!
 
s'(t)=6t-3=6(10)-3=57s instantenous velocity but I don't know how to get average
 
Please don't post the same problem in different forums.

See, you've confused yourself because there may be different replies in your other post.
 
I still need help.
 
sammiyahc0 said:
s'(t)=6t-3=6(10)-3=57s instantenous velocity but I don't know how to get average

Average velocity is defined as change in position divided by time elapsed.
 

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