Passengers board an elevator at the ground floor (i.e., the...

Passengers board an elevator at the ground floor (i.e., the zeroth floor) and take it to the seventh floor, which is 84 feet above the ground floor. The elevator's position $s$ as a function of time $t$ (measured in seconds) is shown in Figure 14. (a) What is the average velocity of the elevator from the time the elevator began moving until the time that it reached the seventh floor? (b) What was the elevator's approximate velocity at time $t=20 ?$ (c) How many stops did the elevator make between the ground floor and the seventh floor (excluding the ground and seventh floors)? On which floors do you think the elevator stopped?

Passengers board an elevator at the ground floor (i.e., the zeroth floor) and take it to the seventh floor, which is 84 feet above the ground floor. The elevator's position $s$ as a function of time $t$ (measured in seconds) is shown in Figure 14.
(a) What is the average velocity of the elevator from the time the elevator began moving until the time that it reached the seventh floor?
(b) What was the elevator's approximate velocity at time $t=20 ?$
(c) How many stops did the elevator make between the ground floor and the seventh floor (excluding the ground and seventh floors)? On which floors do you think the elevator stopped?

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Key Concepts

Graphical Analysis of Motion

Graphical analysis of motion involves interpreting the features of a position-time graph to deduce information about an object's movement. Key aspects include identifying constant slopes that indicate uniform motion, horizontal segments that reflect intervals of rest, and changes in slope that show acceleration or deceleration. This analysis is essential for understanding and describing the dynamics of the motion.

Instantaneous Velocity

Instantaneous velocity is the rate of change of the object's position at a specific moment. It is determined by finding the derivative of the position function or, graphically, by the slope of the tangent line to the position-time curve at that moment, illustrating the object's speed and direction at that exact time.

Average Velocity

Average velocity is defined as the total displacement divided by the total time taken. This concept is used to summarize the overall motion of an object over an interval, capturing its net change in position without regard to any fluctuations during that period.

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