Resource Lesson
Constant Velocity: Position-Time Graphs
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Given below is a strobe picture of a ball rolling across a table. Strobe pictures reveal the position of the object at regular intervals of time, in this case, once each 0.1 seconds.
Notice that the ball covers an equal distance between flashes. Let's assume this distance equals 20 cm and display the ball's behavior on a graph plotting its x-position versus time.
The slope of this line would equal 20 cm divided by 0.1 sec or 200 cm/sec. This represents the ball's average velocity as it moves across the table. Since the ball is moving in a positive direction its velocity is positive. That is, the ball's velocity is a vector quantity possessing both magnitude (200 cm/sec) and direction (positive).
The following physlet by John M. Clement will allow you to test your understanding of this relationship between an object's linear motion and the graphical representation of its behavior.
Position-Time Physlet
Animation created by John M. Clement © 2000 all rights reserved.
Given below are five combinations of position-time graphs for one-dimensional motion. On each graph, the slope represents the object's velocity.
s vs t
- the object is
standing still
at a positive location. Since the slope equals zero it has no movement.
s vs t
- the object is traveling at a constant
positive velocity
. The locations of its position are increasingly positive.
s vs t
- the object is traveling at a constant
positive velocity
but is traveling through a negative region. For example, a car is traveling north on South Clyde Morris Boulevard towards International Speedway.
s vs t
- this slope represents a constant
negative velocity
since the object is traveling in a negative direction at a constant rate. Notice that the locations of its position are becoming less and less positive.
s vs t
- the object is traveling at a constant
negative velocity
through a negative region. For example, a car is traveling south on South Clyde Morris Boulevard towards Dunlawton. The locations of its position are increasingly negative.
Refer to the following information for the next five questions.
Let's practice obtaining information from position-time graphs with the following graph. The y-axis represents position in meters and the x-axis represents time in seconds.
During which intervals was he traveling in a positive direction?
0 to 2 sec
2 to 5 sec
5 to 6 sec
6 to 7 sec
7 to 9 sec
9 to 11 sec
During which intervals was he traveling in a negative direction?
0 to 2 sec
2 to 5 sec
5 to 6 sec
6 to 7 sec
7 to 9 sec
9 to 11 sec
During which interval was he resting in a negative location?
0 to 2 sec
2 to 5 sec
5 to 6 sec
6 to 7 sec
7 to 9 sec
9 to 11 sec
During which interval was he resting in a positive location?
0 to 2 sec
2 to 5 sec
5 to 6 sec
6 to 7 sec
7 to 9 sec
9 to 11 sec
During which two intervals did he travel at the same speed?
0 to 2 sec
2 to 5 sec
5 to 6 sec
6 to 7 sec
7 to 9 sec
9 to 11 sec
Refer to the following information for the next eight questions.
What was his average speed in the first 5 seconds?
What was his average speed in the last 5 seconds?
What was his average velocity during the first 8 seconds?
What was his average velocity from 6 to 10 seconds?
What total distance did he travel?
What was his average speed for the entire 11 seconds?
What was his net displacement for the entire 11 seconds?
What was his average velocity for the entire 11 seconds?
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