# A particle moves along a straight line and has acceleration given by a(t)=t ^2-2 at time t. Its...

## Question:

A particle moves along a straight line and has acceleration given by {eq}a(t)=t ^2-2 {/eq} at time t. Its initial velocity is v(0) = 3 m/s and its initial displacement is s(0) = 1.

a) Find its position function s(t).

## Application of Differential Equation:

If the acceleration function of an object is given, then to find the position function the acceleration function has to be integrated twice. The constants of integration can be determined using the given condition of velocity and displacement.

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Given

A particle is moving along a straight line and its acceleration given by a function {eq}a\left( t \right) = {t^2} - 2{/eq} and its initial...

Second Order Integrated Rate Law

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Chapter 12 / Lesson 6
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Know the relationship between the integrated and differential rate law. Learn about the second-order integrated rate law with examples and a sample question.