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Velocity is an important concept in physics that measures how fast something moves in a specific direction. It is calculated using the formula:

\[ v = \frac{d}{t}\]where:

• \(v\) is the velocity
• \(d\) is the distance traveled
• \(t\) is the time taken

In this exercise, the given distance is \(13.8 \text{ m}\) and the time is \(4.0 \text{ s}\). Plugging these values into the formula gives the nominal velocity:

\[ v = \frac{13.8}{4.0} = 3.45 \text{ m/s}\]This means the body travels at an average speed of 3.45 meters per second. It's important to calculate velocity correctly to understand motion dynamics, which are crucial for predicting the positions and speed of moving objects.

Error propagation is a technique used to estimate the uncertainty in the result, based on the uncertainties in the measurements used to calculate that result. When quantities with uncertainties are used in calculations, these uncertainties affect the precision of the final calculated result.

For division, the formula used for error propagation is:

\[ \frac{\Delta v}{v} = \sqrt{\left(\frac{\Delta d}{d}\right)^2 + \left(\frac{\Delta t}{t}\right)^2}\]where:

• \(\Delta v\) is the absolute error in velocity
• \(\Delta d\) and \(\Delta t\) are the absolute errors in distance and time, respectively

By substituting the given errors \(\Delta d = 0.2\) m and \(\Delta t = 0.3\) s, we calculated the error in velocity as approximately \(0.26 \text{ m/s}\). This means the calculated velocity \(3.45 \text{ m/s}\) could range from \(3.19 \text{ m/s}\) to \(3.71 \text{ m/s}\). Understanding error propagation is vital in scientific experiments to account for measurement errors and to ensure realistic and reliable data.

Percentage error provides a way to express the accuracy of a measurement or calculation relative to the expected or accepted value. It is calculated as:

\[ \text{Percentage Error} = \frac{\Delta v}{v} \times 100\%\]where:

• \(\Delta v\) is the absolute error
• \(v\) is the measured value

In this exercise, substituting the values yielded a percentage error of approximately \(7.54\%\). This gives a clear idea about how much the calculated velocity deviated from the true velocity due to the errors in measured parameters. Evaluating percentage errors helps in assessing the quality of measurements and guides improvements in experimental techniques to achieve more accurate results.