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When discussing the concept of relative speed in physics, we are examining the scenario where two or more objects are moving in a system, and we want to know how fast one object is moving from the perspective of another. What one needs to consider is the direction of the objects’ movements. If two objects are moving in the same direction, the relative speed is the difference between their speeds. Conversely, if they are moving toward each other, their relative speeds add up.

Take, for instance, the textbook problem regarding two cars on a highway. The car in the left lane is travelling faster than the car in the right lane. To calculate the time it takes for the faster car to overtake the slower car, we need to compute their relative speed. You think about it as if you're in the faster car: all you care about is how quickly you're catching up to the car ahead. In this case, since both cars are moving in the same direction, we subtract the speed of the slower car from the speed of the faster car. An important note is that the speeds must be in consistent units, which leads us to the necessity of understanding unit conversions in physics.

In physics, measurements might be given in a range of units, and performing accurate calculations often requires converting these units into a standard or commonly used set. This becomes incredibly important in problems involving motion, like the overtake scenario posed in the textbook question.

For the textbook problem, the speeds of the cars are given in kilometers per hour (km/h), but to proceed with the calculation, we need the speeds to be in meters per second (m/s), which is a more practical unit for such computations. The process involves multiplying by 1000 (since there are 1000 meters in a kilometer) and then dividing by 3600 (since there are 3600 seconds in an hour). This is an essential step because if the units are not consistent, the answer will be incorrect. Remember, misunderstanding or misapplying unit conversion can dramatically change the outcome of a physics problem.

The final part to solving motion problems like our overtaking cars example is to calculate time. The formula universally used in physics is quite straightforward: time equals distance divided by speed. But here we make use of the relative speed we've talked about because we're interested in how quickly the distance between two moving objects closes or increases.

In the textbook problem, the initial separation distance was 100 meters. With the relative speed we calculated, determining how long it takes for the separation distance to reduce to zero, hence for one car to overtake the other, is a simple division. It's essential to provide the time in the appropriate units to match the scenario. In physics, the emphasis on correct unit usage is constant since it ensures the answer will be meaningful in the real world context of the problem.