Question

1 motion: a first look exercises 1 - 5: draw a motion diagram for each motion described below. use the particle model to represent the object as a particle. six to eight dots are appropriate for most motion diagrams. number the positions in order, as shown in figure 4 in the text. 1. a car accelerates forward from a stop sign. it eventually reaches a steady speed of 45 mph. 2. an elevator starts from rest at the 100th floor of the empire state building and descends, with no stops, until coming to rest on the ground floor. (draw this one vertically because the motion is vertical.)

Explanation:

Step1: Analyze car motion

The car starts from rest (initial velocity \(v_0 = 0\)) and accelerates forward until it reaches a steady - speed of 45 mph. In a motion diagram using the particle model, we represent the car as a particle. At the start, the dots are close together as the car has a low speed. As it accelerates, the distance between the dots increases. Once it reaches a steady speed, the dots are evenly spaced.

Step2: Analyze elevator motion

The elevator starts from rest at the 100th floor of the Empire State Building and descends vertically. Similar to the car, at the start, the dots representing the elevator (as a particle) are close together due to low speed. As it accelerates downwards, the distance between the dots increases. When it reaches a constant - speed phase (if any), the dots are evenly spaced, and as it decelerates to come to rest on the ground floor, the dots get closer together again.

Answer:

For the car: Draw a line. Place dots close together at the start, then gradually increase the distance between them until they are evenly spaced when the car reaches a steady speed.
For the elevator: Draw a vertical line. Place dots close together at the top (representing the 100th floor). Increase the distance between the dots as it accelerates downwards, then if it has a constant - speed phase, make the dots evenly spaced, and finally, make the dots close together again as it decelerates to stop at the ground floor.