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      <text>10.4.4 (Example of solving force problem)</text>
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      <text><![CDATA[<h3>Example</h3>

<p> Suppose that the position of a particle at time \(t\) is given by \(x(t)=4t^3 -2t\). What is the force on the object at time \(t=1\) if the mass of the particle is \(3\)kg</p>
 
<h3>Solution</h3>

<p>We have \(x(t)=4t^3 -2t\), so differentiating this gives us the velocity \(v(t) = 12t^2 -2\). Differentiating again gives us acceleration \(a(t) = 24t\). Now, using the second law of motion we have 
\[
F = m \frac{d^2x}{dt} = 3(24t) = 72t. 
\]
thus when \(t=3\) the force is given by \(216N\).</p>]]></text>
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