If a cyclist in the Tour de France travels southwest a total distance of \(12,250 \mathrm{~m}\) in 1 hour, what would the velocity of the cyclist be? A. \(3.80 \mathrm{~m} / \mathrm{s}\) southwest B. \(3.40 \mathrm{~m} / \mathrm{s}\) southwest C. \(3.40 \mathrm{~m} / \mathrm{s}\) northwest D. \(3.80 \mathrm{~m} / \mathrm{s}\) southeast

In physics problems, particularly those involving motion, it's often necessary to convert units of distance and time. Distances might be provided in kilometers, meters, or even miles, while time can be given in seconds, minutes, or hours. For accurate calculations, it’s crucial to convert these into consistent units.
In our exercise, the cyclist travels a distance of 12,250 meters. Fortunately, the distance is already in meters, which is compatible with the SI unit system commonly used in physics.
However, time was provided in hours, which needs to be converted to seconds. One hour equals 60 minutes and one minute equals 60 seconds. Therefore, one hour is calculated as:
1 hour = 60 minutes/hour * 60 seconds/minute = 3600 seconds.
This conversion allows us to use the velocity formula that requires time in seconds.
Always remember to use consistent units to avoid errors in your calculations.

Velocity represents how fast something is moving and in what direction. It's a vector quantity, which means it has both magnitude and direction.
The formula to calculate velocity is: ewline \( v = \frac{d}{t} \), where: \(v\) = velocity, \(d\) = distance traveled, and \(t\)= time taken.
In our exercise, the cyclist's velocity is calculated by: ewline \(v = \frac{12250 \text{ meters}}{3600 \text{ seconds}} \ v \ \frac{12250}{3600} ≈ 3.40 \text{ meters/second} \)
Here, the cyclist’s velocity comes out to be approximately 3.40 meters per second.

In physics, direction is as important as magnitude, especially when dealing with vectors such as velocity. Direction tells us where the object is moving.
In our exercise, the problem states that the cyclist is traveling southwest.
When reporting velocity, include both the calculated magnitude and the given direction. For instance: ewline \( v = 3.40 \text{ meters/second southwest} \)
This way, it’s clear not only how fast the cyclist is moving but also in which direction.
Always double-check the direction before concluding your answer to ensure accuracy in vector quantities.