# A particle moves along an S -axis.Use the given information to find the position function of the...

## Question:

A particle moves along an {eq}S -axis. {/eq} Use the given information to find the position function of the particle

{eq}a)v(t) = 11t^{10} - 10t^{9}; s(0) = 17 \\ b)a(t) = 11 \sin 11t; v(0) = 11; s(0) = 11 {/eq}

## Initial Value Problem:

We know that the derivative of position is velocity and the derivative of velocity is acceleration. Thus the integral of acceleration is velocity and the integral of velocity is position. However, when we integrate we are left with arbitrary constants. In general we can't determine what these constants are, but when we are given initial conditions we can.

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(a) Integrating gives \begin{align} s(t)&=\int v(t) dt \\ &=\int 11t^{10}-10t^9 dt \\ &=t^{11}-t^{10}+C. \end{align} Using the condition...

Initial Value in Calculus: Definition, Method & Example

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Chapter 11 / Lesson 13
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Learn to define the initial value problem and initial value formula. Learn how to solve initial value problems in calculus. See examples of initial value problems.