Calculate average speed/acceleration for the given function

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SUMMARY

The discussion focuses on calculating average speed and acceleration for an object moving along the x-axis, described by the equation x = 3.00t² - 2.00t + 3.00. The average speed between t = 2.00s and t = 3.00s is determined to be 13m, equating average speed with average velocity in this scenario. Additionally, the discussion addresses the need to differentiate between average and instantaneous values for both speed and acceleration at specified time intervals.

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  • Understanding of kinematic equations in physics
  • Familiarity with calculus concepts for instantaneous speed and acceleration
  • Knowledge of average speed and average velocity definitions
  • Ability to perform basic algebraic manipulations
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  • Learn how to calculate instantaneous speed using derivatives
  • Explore the concept of average acceleration and its calculation
  • Investigate conditions under which an object is at rest based on its velocity function
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Alexanddros81
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Homework Statement


Serway Physics Chapter 2

20. An object moves along the x-axis according to the equation ##x=3.00t^2 - 2.00t+3.00##,
where x is in meters and t is in seconds. Determine (a) the average speed between
t=2.00s and t=3.00s, (b) the instantaneous speed at t = 2.00s and at t=3.00s, (c) the average acceleration
between t=2.00s and t=3.00s and (d) the instantaneous acceleration at t=2.00s and t=3.00s.
(e) At what time is the object at rest?

Homework Equations

The Attempt at a Solution



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[/B]
In part (a) I calculated average velocity but it asks for the average speed which is
given by ##v_{avg} = \frac {d} {Δt}## where d is distance traveled between 2 and 3 seconds, which is
13m. So average speed is the same as average velocity in this case.

Is the above correct?
 

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It all looks ok.
 

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