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Year 11 Maths - Methods Differentiation and antidifferentiation of polynomials

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Question 1
84377

The distance, in metres, from a point \(O\) of an object \(t\) seconds after it starts to move in a straight line is given by the function \(s(t)=t^2+3t+1,\,t \ge0\). Find the average rate of change with respect of time of the distance of the object from \(O\) in the first 3 seconds. 

\(6 \text{ m/s}\)

\begin{align}
\text{Average rate of change}&=\frac{s(3)-s(0)}{3-0}\\
&=\frac{(9+9+1)-(1)}{3}\\
&=\frac{19-1}{3}\\
&=6 \text{ m/s}
\end{align}

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