# A particle is moving with the given data. Find the position of the particle. a (t) = cos t + sin...

## Question:

A particle is moving with the given data. Find the position of the particle.

{eq}\displaystyle a (t) = \cos t + \sin t,\ s (0) = 0,\ v (0) = 9 {/eq}.

## Position of Particle:

Velocity is defined as the rate of change of position of the particle and acceleration is defined as the rate of change of velocity. To find the position we have to double integrate the acceleration function.

## Answer and Explanation:

To find the position of the particle we will proceed as

{eq}a(t)=\cos t+\sin t {/eq}

Now to find the velocity we will integrate the acceleration function

{eq}v(t)=\sin t-\cos t+c_{1}\\ v(0)=9\\ 9=-1+C_{1}\\ C_{1}=10\\ v(t)=\sin t-\cos t+10 {/eq}

To find the position we will integrate the velocity function

{eq}s(t)=-\cos t-\sin t+10t+c_{2}\\ 0=-1+c_{2}\\ c_{2}=1\\ s(t)=-\cos t-\sin t+10t+1 {/eq}

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from Physical Science: Middle School

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