PhysicsLAB: Accelerated Motion: Graph Shape Patterns

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 BGraph Cnone 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 AGraph Cnone 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 DGraph EGraph FGraph 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 DGraph EGraph FGraph 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 DGraph EGraph FGraph G

7. Which graph is question #1 would be the correct acceleration-time graph for both questions #5 and #6?

Graph AGraph BGraph Cnone 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 HGraph IGraph JGraph K

9. Which graph or graphs show(s) in question #8 show an object with a positive acceleration?

Graph HGraph IGraph JGraph K

10. Which graph in question #4 could represent a velocity-time graph for Graph J?

Graph DGraph EGraph FGraph G

11. Which graph in question #4 could represent a velocity-time graph for Graph H?

Graph EGraph FGraph GGraph 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.

TrueFalse

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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Resource Lesson:	RL - Accelerated Motion: A Data Analysis Approach RL - Accelerated Motion: Velocity-Time Graphs RL - Analyzing SVA Graph Combinations RL - Average Velocity - A Calculus Approach RL - Chase Problems RL - Chase Problems: Projectiles RL - Comparing Constant Velocity Graphs of Position-Time & Velocity-Time RL - Constant Velocity: Position-Time Graphs RL - Constant Velocity: Velocity-Time Graphs RL - Derivation of the Kinematics Equations for Uniformly Accelerated Motion RL - Derivatives: Instantaneous vs Average Velocities RL - Directions: Flash Cards RL - Freefall: Horizontally Released Projectiles (2D-Motion) RL - Freefall: Projectiles in 1-Dimension RL - Freefall: Projectiles Released at an Angle (2D-Motion) RL - Monkey and the Hunter RL - Summary: Graph Shapes for Constant Velocity RL - Summary: Graph Shapes for Uniformly Accelerated Motion RL - SVA: Slopes and Area Relationships RL - Vector Resultants: Average Velocity
Review:	REV - Test #1: APC Review Sheet
Worksheet:	APP - Hackensack APP - The Baseball Game APP - The Big Mac APP - The Cemetary APP - The Golf Game APP - The Spring Phling CP - 2D Projectiles CP - Dropped From Rest CP - Freefall CP - Non-Accelerated and Accelerated Motion CP - Tossed Ball CP - Up and Down NT - Average Speed NT - Back-and-Forth NT - Crosswinds NT - Headwinds NT - Monkey Shooter NT - Pendulum NT - Projectile WS - Accelerated Motion: Analyzing Velocity-Time Graphs WS - Accelerated Motion: Practice with Data Analysis WS - Advanced Properties of Freely Falling Bodies #1 WS - Advanced Properties of Freely Falling Bodies #2 WS - Advanced Properties of Freely Falling Bodies #3 WS - Average Speed and Average Velocity WS - Average Speed Drill WS - Charged Projectiles in Uniform Electric Fields WS - Chase Problems #1 WS - Chase Problems #2 WS - Chase Problems: Projectiles WS - Combining Kinematics and Dynamics WS - Constant Velocity: Converting Position and Velocity Graphs WS - Constant Velocity: Position-Time Graphs #1 WS - Constant Velocity: Position-Time Graphs #2 WS - Constant Velocity: Position-Time Graphs #3 WS - Constant Velocity: Velocity-Time Graphs #1 WS - Constant Velocity: Velocity-Time Graphs #2 WS - Constant Velocity: Velocity-Time Graphs #3 WS - Converting s-t and v-t Graphs WS - Energy Methods: More Practice with Projectiles WS - Energy Methods: Projectiles WS - Force vs Displacement Graphs WS - Freefall #1 WS - Freefall #2 WS - Freefall #3 WS - Freefall #3 (Honors) WS - Horizontally Released Projectiles #1 WS - Horizontally Released Projectiles #2 WS - Kinematics Along With Work/Energy WS - Kinematics Equations #1 WS - Kinematics Equations #2 WS - Kinematics Equations #3: A Stop Light Story WS - Lab Discussion: Gravitational Field Strength and the Acceleration Due to Gravity WS - Position-Time Graph "Story" Combinations WS - Projectiles Released at an Angle WS - Rotational Kinetic Energy WS - SVA Relationships #1 WS - SVA Relationships #2 WS - SVA Relationships #3 WS - SVA Relationships #4 WS - SVA Relationships #5 WS - Work and Energy Practice: An Assortment of Situations TB - 2A: Introduction to Motion TB - 2B: Average Speed and Average Velocity TB - Antiderivatives and Kinematics Functions TB - Honors: Average Speed/Velocity TB - Kinematics Derivatives TB - Projectile Summary TB - Projectile Summary TB - Projectiles Mixed (Vertical and Horizontal Release) TB - Projectiles Released at an Angle TB - Set 3A: Projectiles