Resource Lesson
Accelerated Motion: Velocity-Time Graphs
Printer Friendly Version
Whenever an object's velocity changes, the object is said to be
accelerating
. If the acceleration occurs while the object is moving in a straight line, then we say that the object is experiencing
rectilinear acceleration
. An example of this type of acceleration occurs whenever an automaker brags that his vehicle can go from 0-60 mph is "x-number" of seconds. He is assuming that you understand that the car is merely gaining speed, not randomly changing speed in a number of different random directions.
When a velocity-time graph lies in the
1st quadrant
, the object is traveling in a
positive direction
. If the line slopes away from the x- or time axis, it is gaining speed; if it slopes towards the x- or time axis, it is losing speed.
gaining speed
+ acceleration
losing speed
- acceleration
constant speed
0 acceleration
If the velocity-time graph lies in the
4th quadrant
, then the object is losing or gaining speed in a
negative direction
.
gaining speed
- acceleration
losing speed
+ acceleration
constant speed
0 acceleration
Notice that graphically, the acceleration is calculated as the slope of each velocity-time graph.
The graph's slope which equals Δy/ Δx can just as easily be expressed as Δv/Δt, or acceleration.
But be careful! Notice that a positive acceleration does NOT always mean that the object is gaining speed. You cannot forget that acceleration is a vector quantity that represents the change in velocity, another vector quantity. Since vectors have two attributes: magnitude and direction, you can use the rules for signed numbers to remember which combinations result in either a positive or a negative acceleration.
gaining speed (+) in a positive (+) direction
+ acceleration
gaining speed (+) in a negative (-) direction
- acceleration
losing speed (-) in a positive (+) direction
- acceleration
losing speed (-) in a negative (-) direction
+ acceleration
The area bounded by the velocity-graph and the nearest x- or time axis tells you the object's displacement during a specified time interval.
As stated before, whenever the graph is in the 1st quadrant, the object is moving in a positive direction and its area represents a positive displacement. Conversely, whenever the graph is in the 4th quadrant, the object is moving in a negative direction and its area represents a negative displacement. During our study, these areas will either be rectangles, triangles, or a combination of triangles and rectangles. You will have the opportunity to practice calculating areas (or displacements) in the following problem.
Let's look at an example to test our understanding of these properties of velocity-time graphs.
Refer to the following information for the next four questions.
During which extended periods of time was he traveling in a positive direction?
0-3
3-5.5
5.5-6.5
6.5-8
8-9
9-13
13-16.5
none of these
During which extended periods of time was he traveling in a negative direction?
0-3
3-5.5
5.5-6.5
6.5-8
8-9
9-13
13-16.5
none of these
During which extended periods of time was he at rest?
0-3
3-5.5
5.5-6.5
6.5-8
8-9
9-13
13-16.5
none of these
During which extended periods of time was he traveling at a constant velocity?
0-3
3-5.5
5.5-6.5
6.5-8
8-9
9-13
13-16.5
Refer to the following information for the next five questions.
During what time interval did he travel the greatest distance?
0-3
3-5.5
5.5-6.5
6.5-8
8-9
9-13
13-16.5
During what time interval did he travel the least non-zero distance?
0-3
3-5.5
5.5-6.5
6.5-8
8-9
9-13
13-16.5
During which time interval(s) did he experience a negative acceleration?
0-3
3-5.5
5.5-6.5
6.5-8
8-9
9-13
13-16.5
During which time interval(s) did he experience a positive acceleration?
0-3
3-5.5
5.5-6.5
6.5-8
8-9
9-13
13-16.5
During which time interval did he experience an acceleration with the greatest magnitude?
0-3
3-5.5
5.5-6.5
6.5-8
8-9
9-13
13-16.5
none of these
Refer to the following information for the next seven questions.
What total distance did he travel in the first 8 seconds?
What total distance did he travel in the last 8.5 seconds?
What was his average speed in the first 8 seconds?
What was his average speed in the last 8.5 seconds?
What was his average speed for the entire 16.5 seconds?
What was his net displacement during the entire 16.5 seconds?
What was his average velocity during the entire 16.5 seconds?
Related Documents
Lab:
Labs -
A Photoelectric Effect Analogy
Labs -
Acceleration Down an Inclined Plane
Labs -
Ballistic Pendulum: Muzzle Velocity
Labs -
Collision Pendulum: Muzzle Velocity
Labs -
Conservation of Momentum
Labs -
Cookie Sale Problem
Labs -
Flow Rates
Labs -
Freefall Mini-Lab: Reaction Times
Labs -
Freefall: Timing a Bouncing Ball
Labs -
Galileo Ramps
Labs -
Home to School
Labs -
InterState Map
Labs -
LAB: Ramps - Accelerated Motion
Labs -
LabPro: Newton's 2nd Law
Labs -
LabPro: Uniformly Accelerated Motion
Labs -
Mass of a Rolling Cart
Labs -
Moment of Inertia of a Bicycle Wheel
Labs -
Monkey and the Hunter Animation
Labs -
Monkey and the Hunter Screen Captures
Labs -
Projectiles Released at an Angle
Labs -
Ramps: Sliding vs Rolling
Labs -
Range of a Projectile
Labs -
Roller Coaster, Projectile Motion, and Energy
Labs -
Rube Goldberg Challenge
Labs -
Target Lab: Ball Bearing Rolling Down an Inclined Plane
Labs -
Terminal Velocity
Resource Lesson:
RL -
Accelerated Motion: A Data Analysis Approach
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: Graph Shape Patterns
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 -
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 -
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
PhysicsLAB
Copyright © 1997-2015
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton