91Ó°ÊÓ

Speed and velocity are fundamental concepts in understanding motion problems related to time, distance, and movement, such as the one given in this exercise. Speed is a scalar quantity that refers to how fast an object is moving, without consideration of the object's direction of travel. It is generally calculated using the formula:

• Speed = Distance / Time

Velocity, on the other hand, is a vector quantity. This means it not only considers the speed of an object but also the direction in which the object is moving. In most introductory motion problems, when direction isn’t specifically mentioned, speed and velocity can be calculated similarly. However, understanding the distinction ensures accurate interpretations in physics problems where direction plays a key role.
This problem shows how to use speed to determine the walking time of different individuals over the same distance, yet under different conditions such as walking normally, using a moving sidewalk, or combining both.

Time and distance are closely linked in problems involving movement. The time it takes to cover a distance can be altered by changing the speed of travel. For instance, in the scenario described, Larry takes 150 seconds to cover the corridor by walking, indicating that his speed is relatively slower compared to the combined speed of walking on a moving sidewalk.
To solve the problem, we identify the relationship:

• Larry’s walking speed: \( v_L = \frac{d}{150} \)
• The moving sidewalk’s speed: \( v_m = \frac{d}{70} \)

These equations reflect how effectively time and distance interact in motion problems.
When you calculate time by rearranging the formula to Time = Distance / Speed, you see how changes in either distance or speed will affect time. Here, the strategic combination of walking speed and sidewalk speed allows Moe to traverse the same distance more quickly than Larry.

Relative motion is crucial when analyzing how different elements in a system contribute to overall speed. In this problem, Moe's motion on the moving sidewalk combines both his walking speed and the sidewalk's speed.
Relative motion considers how one object's movement compares or adds to another's. In practical terms, Moe's total speed becomes a sum, allowing calculations to involve multiple motion influences:

• Moe’s total speed: \( v_M = v_L + v_m \)

By adding the speeds, you account for both his individual walking speed and the moving sidewalk’s speed.
Then, to find the time Moe takes, rearrange the formula as shown:

• \( \frac{1}{t_M} = \frac{1}{150} + \frac{1}{70} \)

This equation uses the concept of inverse addition for relative speeds, leading to the calculation of endpoint time, which represents how relative motion can simplify time in dynamic systems.