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Calculating distance is crucial when determining how far an object or person travels over a certain period. In motion problems, like the bicyclist's trip from the exercise, this is usually done using the formula: \[ \text{Distance} = \text{Speed} \times \text{Time} \] This formula allows us to compute the distance by multiplying the average speed by the time taken for each segment of the journey.

• For the first part of the trip, with a speed of \(7.2\, \mathrm{m/s}\) over \(1320\, \mathrm{s}\), the distance is \(9504\, \mathrm{m}\).
• The second part, with a speed of \(5.1\, \mathrm{m/s}\) over \(2160\, \mathrm{s}\), calculates to \(11016\, \mathrm{m}\).
• For the final part, at \(13\, \mathrm{m/s}\) over \(480\, \mathrm{s}\), the distance comes to \(6240\, \mathrm{m}\).

By breaking down the journey into sections and calculating each separately, you ensure accuracy. Then, sum these distances for the total distance traveled: \[ 9504\, \mathrm{m} + 11016\, \mathrm{m} + 6240\, \mathrm{m} = 26760\, \mathrm{m} \] This calculation shows the bicycle trip covered a total of \(26760\, \mathrm{meters}\).

Unit conversion is an essential skill in solving physics problems, especially when dealing with speed and time. It's important that all units are consistent before inserting them into formulas. In the exercise, time was initially given in minutes but needed to be converted into seconds. Here's why: - Speed is provided in meters per second (\(\mathrm{m/s}\)), requiring time to be in seconds for a coherent calculation.To convert from minutes to seconds, multiply by 60 (since each minute contains 60 seconds):

• 22 minutes: \(22 \times 60 = 1320 \) seconds.
• 36 minutes: \(36 \times 60 = 2160 \) seconds.
• 8 minutes: \(8 \times 60 = 480 \) seconds.

With time converted to seconds, calculations such as distance and average velocity can proceed without discrepancies. Consistently using the correct units avoids errors and ensures clear communication of the results.

Motion in a straight line is a fundamental topic in physics, dealing with the simplest form of movement where an object travels along a straight trajectory. In situations like the bicyclist's trip, the path is a straight road, and all movement occurs in one direction (north in this case). This simplifies calculations, as one-dimensional motion only requires consideration of distance, speed, and time without having to account for changes in direction. Key aspects include:

• Understanding scalar quantities: Distance and speed are scalar quantities, only having magnitude, making them straightforward to handle in straight-line motion.
• Using constant speeds: The exercise lists constant speeds for each part of the trip, simplifying the calculations since there are no accelerations or decelerations to consider.
• Computing average velocity: With scalar quantities and a constant direction, the average velocity is the same as average speed (when the entire motion is along a single straight path).

Understanding these basics in straight-line motion allows students to grasp other motion concepts more easily, building a strong foundation for more complex physics topics.