Question

constant velocity
(9pts, 1.5 each graph)
use the ophysics link on google classroom to explore position and velocity graphs.

1. set x (position), v (velocity), and a (acceleration) as indicated.
2. copy the graphs for position and velocity (do not copy acceleration graph)
3. describe the shape of the graph. (horizontal, sloped, positive, negative, etc)

constant velocity
at rest (v=0)
xi=1
vi=0
a_i=0
position
0
time
xi=1
shape:
velocity
0
time
vi=0
shape:
moving forward,
constant positive
velocity
xi=1
vi=1
a_i=0
position
0
time
xi=1
shape:
velocity
0
time
vi=1
shape:
moving backwards,
constant negative
velocity
xi=1
vi=-1
a_i=0
position
0
time
xi=1
shape:
velocity
0
time
vi=-1
shape:

Explanation:

Step1: Analyze "At Rest (v=0)" Position Graph

For an object at rest (\(v = 0\)), position \(x\) does not change with time. So the position - time graph should be horizontal (no slope) because \(x\) is constant (\(x_i=1\)) as time increases.

Step2: Analyze "At Rest (v=0)" Velocity Graph

Velocity is \(0\) and constant, so the velocity - time graph is a horizontal line at \(v = 0\) (since velocity doesn't change with time).

Step3: Analyze "Moving forward, constant positive velocity" Position Graph

When velocity \(v = 1\) (constant and positive), position \(x\) changes linearly with time (\(x=x_i + vt\), here \(x_i = 1\), \(v = 1\), so \(x=1 + t\)). A linear relationship between \(x\) and \(t\) gives a sloped (straight line with positive slope) position - time graph.

Step4: Analyze "Moving forward, constant positive velocity" Velocity Graph

Velocity is constant (\(v = 1\)) and positive, so the velocity - time graph is a horizontal line at \(v = 1\) (no change in velocity with time).

Step5: Analyze "Moving backwards, constant negative velocity" Position Graph

When velocity \(v=- 1\) (constant and negative), position \(x\) changes linearly with time (\(x=x_i+vt=1 - t\)). This is a linear relationship with a negative slope, so the position - time graph is a sloped (straight line with negative slope) graph.

Step6: Analyze "Moving backwards, constant negative velocity" Velocity Graph

Velocity is constant (\(v = - 1\)) and negative, so the velocity - time graph is a horizontal line at \(v=-1\) (no change in velocity with time).

Answer:

• At Rest (v = 0):
• Position Graph Shape: Horizontal (constant position)
• Velocity Graph Shape: Horizontal (at \(v = 0\))
• Moving forward, constant positive velocity (\(v = 1\)):
• Position Graph Shape: Sloped (positive slope, linear increase)
• Velocity Graph Shape: Horizontal (at \(v = 1\))
• Moving backwards, constant negative velocity (\(v=-1\)):
• Position Graph Shape: Sloped (negative slope, linear decrease)
• Velocity Graph Shape: Horizontal (at \(v=-1\))