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An object moves along the x axis according to the equation x = 3.90t^2 - 2.00t + 3.00, where x is...

Question:

An object moves along the x axis according to the equation x = 3.90t{eq}^{2} {/eq} - 2.00t + 3.00, where x is in meters and t is in seconds.

(a) Determine the average speed between t = 2.80 s and t = 4.60 s.

(b) Determine the instantaneous speed at t = 2.80 s.

Determine the instantaneous speed at t = 4.60 s.

(c) Determine the average acceleration between t = 2.80 s and t = 4.60 s.

(d) Determine the instantaneous acceleration at t = 2.80 s. Determine the instantaneous acceleration at t = 4.60 s.

Instantaneous velocity and acceleration:

Instantaneous velocity = {eq}v\ =\ \dfrac{dx}{dt} {/eq}

Instantaneous acceleration = {eq}a\ =\ \dfrac{dv}{dt} =\ \dfrac{d^2x}{dt^2} {/eq}

Answer and Explanation:

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Given,

{eq}x\ =\ 3.90t^2\ -\ 2.0t\ +\ 3.0 {/eq}

part (a)

{eq}(x)_{4.60}\ =\ 3.90\times 4.60^2\ -\ 2\times 4.60\ +\ 3.0\\\ \Rightarrow (x)_{4.60}\...

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What Is Motion? - Definition & Equations

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Chapter 9 / Lesson 1
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After watching this video, you will be able to explain what motion is and use basic equations of motion to solve problems. A short quiz will follow to test your knowledge.


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