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Displacement is a crucial concept in physics, especially when discussing motion. It refers to how far out of place an object is; it is the object's overall change in position. Unlike distance, which only considers how much ground has been covered, displacement is concerned with the direction as well. This makes displacement a vector quantity, meaning it has both magnitude and direction.
For example, in the problem mentioned, the man ran 2.40 km. However, his displacement is recorded as 2.40 km towards the east because this direction is specified. Always remember that when you talk about displacement, you're indicating not just how far, but also in what direction.

Understanding the proper conversion of time is essential in physics problems, particularly those involving velocity, where consistent units are crucial. For many calculations, time must be converted to the same unit as other parameters involved. For velocity equations, time is most commonly converted into seconds.
In our exercise scenario, we are given a time period of 25 minutes. To convert this into seconds, we multiply by 60, as there are 60 seconds in a minute. So, 25 minutes becomes 1500 seconds. Using seconds for time ensures that the units for time and distance match, facilitating seamless calculation of velocity.

A vector quantity is one that includes both magnitude and direction. This is in contrast to scalar quantities, which only have magnitude. Understanding vectors is essential for discussing physical phenomena that are not purely referenced by a single measurement.
Displacement, as discussed, is a vector quantity. Similarly, velocity is another example, as it involves both the speed (a scalar) and the direction of motion. In practical terms, specifying these vectors aids in accurately describing and predicting physical movement, like the man running east at a certain speed. Remembering the dual nature of vectors is key to interpreting and solving physics problems effectively.

The velocity formula is a foundational aspect of physics, used to calculate how fast something is moving with respect to both time and direction. The average velocity can be calculated using the formula:

• \( v_{avg} = \frac{\text{displacement}}{\text{time}} \)

This formula expresses the rate of change of an object's position. In our specific problem, you know the displacement (2.40 km east) and the time period (25 minutes or 1500 seconds in seconds).
You convert the displacement to meters (2400 meters) and subsequently divide by the total time in seconds to determine the average velocity.
Thus, using:

• \( v_{avg} = \frac{2400 \text{ m}}{1500 \text{ s}} = 1.6 \text{ m/s} \)

This result is an indication that, on average, the man moved eastward at a speed of 1.6 meters per second, combining both magnitude and direction, characteristic of a vector quantity.