| Excerpt | ||
|---|---|---|
| ||
Determining the relationships between position, velocity and acceleration from a position vs. time plot. |
| Composition Setup |
|---|
By looking at the position versus time graph shown above, determine the following at each of the eight numbered instants of time:
A.) Is the object's position positive or negative?
B.) Is the object's velocity positive or negative?
C.) Is the object's acceleration positive or negative?
D.) Is the object speeding up (accelerating) or slowing down (decelerating)?
Solution
System, Interactions and Model: This exercise is a review of the definitions of position, velocity and acceleration. These concepts are used in several of the models in the hierarchy.
| Toggle Cloak | ||
|---|---|---|
|
| Cloak | |||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| |||||||||||||||||||||||||||||||||||||||||||||
It is important to note that any combination of signs is possible for position, velocity and acceleration! | |||||||||||||||||||||||||||||||||||||||||||||
| Wiki Markup | |||||||||||||||||||||||||||||||||||||||||||||
| {excerpt:hidden=true}Determining the relationships between position, velocity and acceleration from a position vs. time plot.{excerpt}
{table:align=right|cellspacing=0|cellpadding=1|border=1|frame=box|width=30%}
{tr}
{td:align=center|bgcolor=#F2F2F2}*[Examples from Motion and Acceleration]*
{td}
{tr}
{tr}
{td}
{pagetree:root=Examples from Kinematics}
{search-box}
{td}
{tr}
{table}
!accelvelpos.gif!
{composition-setup}{composition-setup}
By looking at the position versus time graph shown above, determine the following at each of the eight numbered instants of time:
A.) Is the object's position positive or negative?
B.) Is the object's velocity positive or negative?
C.) Is the object's acceleration positive or negative?
D.) Is the object speeding up (accelerating) or slowing down (decelerating)?
h4. Solution
*System, Interactions and Model:* [excerpt]This exercise is a review of the definitions of position, velocity and acceleration.[excerpt] These concepts are used in several of the models in the hierarchy.
{toggle-cloak:id=answers} *Answers:*
{cloak:id=answers}
{table}{tr}{th}{th}{th:align=center|bgcolor=#F2F2F2}Time 1{th}{th:align=center|bgcolor=#F2F2F2}Time 2{th}{th:align=center|bgcolor=#F2F2F2}Time 3{th}{th:align=center|bgcolor=#F2F2F2}Time 4{th}{th:align=center|bgcolor=#F2F2F2}Time 5{th}{th:align=center|bgcolor=#F2F2F2}Time 6{th}{th:align=center|bgcolor=#F2F2F2}Time 7{th}{th:align=center|bgcolor=#F2F2F2}Time 8{th}{tr}
{tr}{th:align=center|bgcolor=#F2F2F2}Position{th}{td:align=center}+{td}{td:align=center}+{td}{td:align=center}+{td}{td:align=center}+{td}{td:align=center}--{td}{td:align=center}--{td}{td:align=center}--{td}{td:align=center}--{td}{tr}
{tr}{th:align=center|bgcolor=#F2F2F2}Velocity{th}{td:align=center}+{td}{td:align=center}+{td}{td:align=center}--{td}{td:align=center}--{td}{td:align=center}--{td}{td:align=center}--{td}{td:align=center}+{td}{td:align=center}+{td}{tr}
{tr}{th:align=center|bgcolor=#F2F2F2}Acceleration{th}{td:align=center}+{td}{td:align=center}--{td}{td:align=center}--{td}{td:align=center}+{td}{td:align=center}--{td}{td:align=center}+{td}{td:align=center}+{td}{td:align=center}--{td}{tr}
{tr}{th:align=center|bgcolor=#F2F2F2}Acceleration/\\Deceleration{th}{td:align=center}A{td}{td:align=center}D{td}{td:align=center}A{td}{td:align=center}D{td}{td:align=center}A{td}{td:align=center}D{td}{td:align=center}A{td}{td:align=center}D{td}{tr}{table}
{note}It is important to note that *any* combination of signs is possible for position, velocity and acceleration!{note}
{cloak} |