The position of a pinewood derby car was observed at various...

The position of a pinewood derby car was observed at various moments; the results are summarized in the following table. Find the average velocity of the car for (a) the first 1-s time interval, (b) the last 3 s, and (c) the entire period of observation. $$ \begin{array}{lllllll}\hline t(\mathbf{s}) & {0} & {1.0} & {2.0} & {3.0} & {4.0} & {5.0} \\ \hline x(\mathbf{m}) & {0} & {2.3} & {9.2} & {20.7} & {36.8} & {57.5} \\ \hline\end{array} $$

The position of a pinewood derby car was observed at various moments; the results are summarized in the following table. Find the average velocity of the car for (a) the first 1-s time interval, (b) the last 3 s, and (c) the entire period of observation.
$$
\begin{array}{lllllll}\hline t(\mathbf{s}) & {0} & {1.0} & {2.0} & {3.0} & {4.0} & {5.0} \\ \hline x(\mathbf{m}) & {0} & {2.3} & {9.2} & {20.7} & {36.8} & {57.5} \\ \hline\end{array}
$$

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Key Concepts

Time Interval

A time interval is a specific period during which measurements are taken or events occur. When calculating average velocity, the duration of the time interval over which the displacement occurs is used in the denominator of the velocity calculation. Understanding the time interval is fundamental to resolving questions that involve changes in motion over different segments of time.

Displacement

Displacement refers to the change in position of an object, calculated as the difference between its final and initial positions. Unlike distance, displacement is a vector quantity, meaning it carries both magnitude and direction. In the context of average velocity, only the net change in position is used to determine how quickly and in what direction the object is moving.

Average Velocity

Average velocity is a measure of the rate at which an object changes its position over a specified time interval. It is calculated as the displacement (the difference between the final and initial positions) divided by the time over which the displacement occurs. This concept is crucial for understanding motion because it provides a single value representing the overall rate of change, regardless of variations in instantaneous speed between observations.

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