A car travels at 22.0 mph for 15.0 min and 35.0 mph for \(30.0 \mathrm{~min}\). How far does it travel overall? a) \(23.0 \mathrm{~m}\) b) \(3.70 \cdot 10^{4} \mathrm{~m}\) c) \(1.38 \cdot 10^{3} \mathrm{~m}\) d) \(3.30 \cdot 10^{2} \mathrm{~m}\)

Understanding unit conversion is essential in physics, especially when calculating distances. When dealing with time, speed, and distance, it is important to ensure that all units are consistent to avoid errors. For example, speeds may be given in miles per hour, but time might be in minutes or even seconds. To accurately calculate distances, we must convert all units to align—typically to the base International System of Units (SI).

In our exercise, the car's speeds were given in miles per hour (mph), and the time was in minutes. To make them compatible, we converted time into hours since the speed was per hour. To do this, we divided the number of minutes by 60, as there are 60 minutes in an hour. Knowing that an hour is the base unit for the given speed (mph), this conversion is vital for accurate calculations. Similarly, distances calculated in miles must be converted to meters to match the answer options, utilizing the conversion factor where 1 mile equals 1,609.34 meters.

The relationship between speed, time, and distance is one of the cornerstones of kinematics in physics. The basic equation connecting these three variables is: \[ \text{Distance} = \text{Speed} \times \text{Time} \].This formula allows us to solve problems where we need to find any one of the variables, as long as the other two are known.

In our case, we used this relationship to find the distance traveled by the car in each segment of the journey. By multiplying the speed of the car by the time traveled, which we had already converted to hours, we found the distance in miles. Then, we added the distances of both segments together to find the total distance covered by the car. This step-by-step approach is essential for breaking down complex problems into more manageable parts.

Kinematics is the branch of physics that deals with the motion of objects without considering the forces that cause such motion. It involves analyzing the positions, velocities, and accelerations of moving objects. In our problem, we looked at a simple case where kinematics principles apply to calculate the total distance traveled by a car moving at constant speeds over different time intervals.

By applying the fundamental kinematics equation for distance calculation, and ensuring correct unit conversions, we determined the car's total travel distance, showcasing a practical application of kinematics in a real-world scenario. Understanding these concepts together forms a strong foundation for more advanced studies in physics and mechanics, where variables may change over time and motion may be influenced by various forces.