Worksheet
Accelerated Motion: Graph Shape Patterns
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Refer to the following information for the next three questions.
Use your flash cards, or the lesson on graph shapes, to answer each of the following questions.
A
B
C
1. Each of the following graph shapes is a horizontal line. What general information does this say about the y-axis variable being graphed?
the variable's value is always positive throughout the time interval displayed on the graph
the variable's value is always negative throughout the time interval displayed on the graph
the variable's value remains constant throughout the time interval displayed on the graph - it does not increase or decrease
2. Suppose Graph A in question #1 represents a position-time graph. Which graph in question #1 would present its correct velocity-time graph?
Graph B
Graph C
none of the original three
3. Suppose Graph B in question #2 represents a velocity-time graph. Which graph in question #1 would present its correct acceleration-time graph?
Graph A
Graph C
none of the original three
Notes:
Hopefully you have now noticed these two relationships
s-t graph
slope of s-t graph
v-t graph
slope of v-t graph
a-t graph
We define:
velocity
to be the rate of change of displacement and
acceleration
to be the rate of change of velocity.
In questions #2 and #3, you determined that when an object's position does not change, its velocity is zero; and when an object's velocity does not change, its acceleration is zero.
Refer to the following information for the next four questions.
Use your flash cards, or the lesson on graph shapes, to answer each of the following questions.
D
E
F
G
4. Which of the graph or graphs shown above could represent a velocity-time graph of an object traveling in a positive direction?
Graph D
Graph E
Graph F
Graph G
5. Which of the graphs shown above could represent the velocity-time graph for an object uniformly losing speed in a positive direction?
Graph D
Graph E
Graph F
Graph G
6. Which of the graphs shown in question #4 would represent the velocity-time graph for an object uniformly gaining speed in a negative direction?
Graph D
Graph E
Graph F
Graph G
7. Which graph is question #1 would be the correct acceleration-time graph for both questions #5 and #6?
Graph A
Graph B
Graph C
none would be correct
Notes:
Hopefully you have now noticed this relationship
v-t graph
slope of v-t graph
a-t graph
Since acceleration is the rate of change of velocity (or the slope of a velocity-time graph), an object can experience a
positive acceleration
by either:
gaining speed (+) in a positive direction (+)
(+) x (+) = (+)
losing speed (-) in a negative direction (-)
(-) x (-) = (+)
Since velocity and acceleration are vectors, the rules of "signed numbers" can assist in remembering when an acceleration will be positive or negative.
No longer can you simply think of acceleration as gaining speed and decelerating as losing speed. You MUST also consider the object's direction of motion.
Refer to the following information for the next five questions.
Use your flash cards, or the lesson on graph shapes, to answer each of the following questions about the following position-time graphs.
H
I
J
K
8. Which graph or graphs show(s) an object moving in a positive direction?
Graph H
Graph I
Graph J
Graph K
9. Which graph or graphs show(s) in question #8 show an object with a positive acceleration?
Graph H
Graph I
Graph J
Graph K
10. Which graph in question #4 could represent a velocity-time graph for Graph J?
Graph D
Graph E
Graph F
Graph G
11. Which graph in question #4 could represent a velocity-time graph for Graph H?
Graph E
Graph F
Graph G
Graph H
12. Both Graph J and Graph H represent an object uniformly losing speed. Graph J has a negative acceleration while Graph H has a positive acceleration.
True or False: Since acceleration is a vector, the fact that they are traveling in opposite directions reverses the sign.
True
False
Notes:
Hopefully you have now noticed these two relationships
Graphs H and I form the two "halves" of a
parabola that opens upward
. They represent situations in which the
acceleration is positive
.
Graphs J and K form the two "halves" of a
parabola that opens downward
. They represent situations in which the
acceleration is negative
.
Remember that
acceleration can be calculated as the slope of a velocity-time graph
. The velocity graphs that correspond to Graphs H and I have
positive slopes
. While those corresponding to J and K have
negative slopes
.
Whenever an object is
losing speed
, its velocity graph moves
towards the x-axis
(where velocity = zero). When it is
gaining speed
, its velocity graph moves
away from the x-axis
to values on the y-axis that represent "greater" speeds.
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