Introduction to Motion Position-Time Graphs Velocity-Time Graphs Acceleration-Time Graphs.
Velocity Time Graphs. What do Position Time graphs show? They show how position changes with time....
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Transcript of Velocity Time Graphs. What do Position Time graphs show? They show how position changes with time....
What do Position Time graphs show?
• They show how position changes with time.
• So far we have studied graphs that show uniform motion. Or a constant velocity.
• We have seen some graphs that change slope, but they do this instantaneously.
• This is an unrealistic way to view the world.
What does a changing d t graph look like?
• This we don’t have the tools to work with a graph like this it varies too much.
How do we read a curve on a d t graph?
• Look at how the slope is changing.• The best way to do this is to find the slope
at several points along the curve.• The slope of a curve at any point can be
found by drawing a tangent at that point.
The slope of a Tangent
• Tangent is any line that just touches the curve at that point.
• Looking at the tangent line you can tell that the slope is increasing from point 1 to point 3
1
2
3
What does a changing slope on a d t graph mean?
• Slope on a d t graph is the velocity of the object.
• So a changing slope means a changing velocity!
This graph has an increasing slope so that means the velocity is increasing or has a positive change.
This graph has a decreasing slope so that means the velocity is decreasing or has a negative change.
What about these?
• These can blow your mind unless you apply the tangent model.
This graph starts off with a steep negative slope and goes to a shallower slope. The velocity has a high negative value and goes to a smaller negative value. This is a positive change in velocity.
This graph starts off with a shallow negative slope and goes to a steep negative slope. The velocity has a low negative value and goes to a high negative value. This is a negative change in velocity.
Now what?
• These curved graphs are fine to understand the motion qualitatively however, they are not very useful quantitatively.
• Since these graphs are continuously or consistently changing. Then they too, are a form of uniform motion. A uniformly changing motion.
• Lets see how a d t graph translates into a v t graph.
Exploring a v t Graph• What does a linear d t graph
look like as a v t?
v→(m/s)
t (s)
4
5
d→(m)
t (s)
20
5
Slope = 4 m/s
A constant slope means a constant or unchanging velocity. That translates into a horizontal v t graph.
A changing d t graph
• If the d t graph is uniformly changing in the positive direction.• You can tell the change by looking at how the tangent changes!• Then the velocity is consistently changing.• Which translates into a positively sloped straight line.
Positively changingvelocity
Positive acceleration
D (m)
V (m/s)
Horizontal = 0 velocity
Steep slope = high velocity
Starting at 0 velocity
Ending at a high velocity
A changing d t graph
• If the d t graph is uniformly changing in the positive direction.• Then the velocity is consistently changing.• Which translates into a positively sloped straight line.• When velocity reaches maximum value it remains constant• Constant velocity means 0.00 acceleration = horizontal line
Positively changingvelocity
Positive acceleration
D (m)
V (m/s)
Constant velocity
Constant velocity
A changing d t graph
• If the d t graph is uniformly changing in the negative direction.• You can tell the change by looking at how the Tangent changes!• Then the velocity is consistently changing negatively.• Which translates into a negatively sloped straight line.
Negatively changingvelocity
Negative accelerationD
(m)
V (m/s)
Vertical = High velocity
Low slope = low velocity
Starting at a high velocity
Ending at a low velocity
A negatively changing d t graph
• If the d t graph is uniformly changing in the negative direction.
• You can tell how it is changing by looking at the Tangent.• Then the velocity is consistently changing.• Which translates into a negatively sloped straight line.
XX
Yes, we have a straight line again!
• We have a burning desire to calculate the slope.
• Slope of a v t graph would be….• Slope = rise = ∆v
run ∆t• This value will measure the rate of change
of velocity with time.• This is known as acceleration!
Exploring Acceleration
• This term describes how velocity changes with time.
• Acceleration is a vector quantity.• Units: m m x 1 m
s = s s = s2
s• What does 5.0 m/s2 mean?• It means that the velocity changes by + 5.0 m/s
every second.
What about deceleration?
• Avoid using this term altogether!• Why?• Deceleration indicates slowing down
toward zero velocity. • This would also inherently imply a
negative velocity.• This is not always true!
Lets See
• This is deceleration on a v t graph.• This object has a decreasing velocity
ending at zero.
What happens here?
• If we extend the deceleration graph beyond the zero velocity the object has an increasing velocity in the negative direction.
• This is NOT what deceleration means.
Deceleration
Acceleration in the negative direction.
What happens here?
• If there is a negative velocity to decelerate the object needs to have a positive change in velocity to reach zero velocity. This is a positive deceleration which doesn’t make sense!
Deceleration (positive)
Acceleration
Solution
• Always use acceleration: the rate of change of velocity with time. A vector quantity.
Acceleration in the negative direction. - a
Acceleration in the positive direction. + a