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Motion describes the change in position of objects over time. Every moving object experiences some form of motion, whether linear, rotational, or oscillatory. In physics, motion is usually considered with respect to a reference point. For example, a car driving down the road appears to be moving forward from the perspective of a stationary observer on the sidewalk. However, that same car might seem completely still to a passenger.
In our case, both Prius and Passat are in motion, traveling towards one another. The state of motion is described relative to each other, which leads us to the concept of relative velocity. Distances between the cars change depending on their directions and speeds, which will determine the time it takes for them to meet or pass each other completely. Therefore, motion and its comprehension are fundamental to understanding the observed relative velocity.

Velocity is a vector that indicates both the speed and direction of an object's motion. Speed is a scalar quantity, focusing only on how fast an object is moving, with no concern for direction, whereas velocity takes both into consideration.
In this context, the velocity of the Toyota Prius and the VW Passat needs not only to consider their speeds—65 mph and 42 mph, respectively—but also the directions they are traveling. The Prius heading north and the Passat heading south tells us they are moving in opposite directions. The velocity can be positive in one direction and negative in the other, depending on the chosen frame of reference. This variance in direction is essential for calculating relative velocity.

Vectors are quantities defined by both magnitude and direction, and they play a crucial role in understanding motion and velocity. Examples include displacement, velocity, acceleration, and force. They are usually represented graphically with arrows, where the length of the arrow reflects the vector's magnitude, and its direction shows the vector's direction.
In analyzing the problem, we use vector addition to calculate relative velocity. While the Prius moves north at 65 mph and the Passat moves south at 42 mph, their velocities can be represented as vectors pointing in opposite directions. By adding these vectors (since they are in opposite directions), we arrive at a combined relative velocity of 107 mph. This result helps us visualize how vectors simplify solving such problems and clarify the combined motion of the two cars.

Distance in physics represents how far apart objects are. It is a scalar quantity, only considering the magnitude without any direction. In the provided problem, the distances of 250 feet and 525 feet were given to describe the intervals at which the velocities are questioned.
It is important to note that while distance changes as the cars move, relative velocity remains constant unless there are speed changes. This particular problem assumes constant speeds, so regardless of the distance between the Prius and the Passat, their relative velocity does not vary. Such an understanding underscores the independence of relative velocity from distance, provided that the speeds of the observed objects remain unchanged.