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NSW Y12 Maths - Advanced Motion and Rates Average Velocity and Speed

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Average Velocity and Speed Theory

$\begin{aligned} & \text { Average velocity }=\frac{x_2-x_1}{t_2-t_1} \\ \\ & \text { Average speed }=\left|\frac{x_2-x_1}{t_2-t_1}\right| \end{aligned}$\\ \begin{multicols}{2} \textbf{Example 1}\\ A particle is moving with displacement function \(x=3 t^2+4\), where \(t\) is the time in seconds and the displacement \(x\) is in metres. Find the average velocity in the first 3 seconds.\\ \textbf{Example 1 solution}\\ $\begin{aligned} & t=0 \qquad x=4 \\ & t=3 \qquad x=3 \times 3^2+4 \\ & \qquad\qquad\quad=13 \\ & \text { Average velocity }=\frac{13-4}{3-0} \\ &\qquad\qquad\qquad\qquad =3 \mathrm{~m} / \mathrm{sec} \end{aligned}$\\ \columnbreak \textbf{Example 2}\\ A particle is moving with displacement function \(x=2-5 t\), where \(t\) is the time in seconds and the displacement \(x\) is in metres. Find the average speed in the first 3 seconds.\\ \textbf{Example 2 solution}\\ $\begin{aligned} & t=0 \qquad x=2 \\ & t=3 \qquad x=2-5 \times 3 \\ & \qquad\qquad\quad=-13 \\ & \text { Average speed }=\left|\frac{-13-2}{3-0}\right| \\ & \qquad\qquad\qquad\quad=5 \mathrm{~m} / \mathrm{sec} \end{aligned}$\\ \end{multicols}

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  • Average Velocity and Speed - Video - Example Problems on Average Speed and Average Velocity

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