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Displacement is an important concept in physics that represents the change in position of an object. Unlike distance, which is a scalar quantity and only considers the magnitude, displacement is a vector quantity. This means it takes into account both the magnitude and the direction of the movement. In the exercise above, displacement is concerned with the straight-line distance traveled along a specified path.
For example, in case (a), the person moves a total displacement of 146.4 meters (walking 73.2 m and then running 73.2 m along a straight track). Displacement is straightforward as it does not depend on the specific days or paths taken—only the initial and final positions matter.
This distinction means that regardless of the speed or time taken, the displacement is simply the total direct length from start to finish along the path.

Calculating the time taken for different parts of motion is essential for determining factors like velocity. Time can be simply calculated using the formula:

• \( t = \frac{d}{v} \)

This formula indicates time \( t \) varies directly with distance \( d \) and inversely with velocity \( v \).
In case (a), the time for walking is calculated as 60 seconds using the distance of 73.2 meters at a velocity of 1.22 m/s. Similarly, the running time is 24 seconds for the same distance at a velocity of 3.05 m/s.
In case (b), each phase (walking and running) is measured in equal time durations of 60 seconds despite differences in distance covered due to the differing velocities. This understanding helps decide the total time duration for combined movements in real-world problems.

Creating a graph of motion involves plotting position against time, which visually conveys how motion takes place. This can be particularly helpful in comparing different phases or scenarios of movement.
For cases (a) and (b), the task involves plotting distance (displacement \( x \)) on the vertical axis and time (\( t \)) on the horizontal axis. The graph visually represents the distance traveled over time:

• For case (a), starting at the origin, the graph rises to 73.2 meters in 60 seconds (the walking phase) and then continues to rise linearly to 146.4 meters by 84 seconds (including the running phase).
• For case (b), the graph progresses from 0 to 73.2 meters in 60 seconds and further climbs to 256.2 meters by 120 seconds. This reflects a faster overall movement due to a longer running distance.

The slope of each line segment shows the speed during that time interval, and overall trends show the proportionality between time and displacement.

Physics problems often involve applying equations and graphical understanding to solve questions related to motion. In these problems, understanding the relationships between different physical quantities like velocity, distance, and time is crucial.
This type of exercise tests your comprehension of motion concepts and your ability to integrate various mathematical elements into a congruent solution. Breaking the problem into manageable parts like calculating individual times, total distances, and interpreting graph details facilitates solutions. The use of clearly defined formulas like for velocity \( v_{avg} = \frac{d_{total}}{t_{total}} \), is critical. This allows you to clearly understand ideas and derive correct results efficiently.
Through practice, physics exercises become less about rote memorization and more about developing an intuition for how objects move and relate to each other.