Motion and Differential Calculus

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Motion and Differential Calculus

• Instantaneous velocity
• Instantaneous acceleration

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Motion and Differential Calculus
In preparing for class today I spent a total of
____ hours on reading, homework, and the Student
Workbook.

• Zero
• ½ an hour
• 1 ½ hours
• 2 hours
• 2 ½ hours
• 3 hours
• Over 3 hours

3
Motion and Differential Calculus
The slope at a point on a position-versus-time
graph of an object is
1) the objects speed at that point. 2) the
objects average velocity at that point. 3) the
objects instantaneous velocity at that point. 4)
the objects acceleration at that point. 5) the
distance traveled by the object to that point.
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Motion and Differential Calculus
The slope at a point on a position-versus-time
graph of an object is
1) the objects speed at that point. 2) the
objects average velocity at that point. 3) the
objects instantaneous velocity at that point. 4)
the objects acceleration at that point. 5) the
distance traveled by the object to that point.
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Motion and Differential Calculus
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Motion and Differential Calculus
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Motion and Differential Calculus
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Motion and Differential Calculus
So far we have been talking about average
velocity. What about the velocity at an instant,
instantaneous velocity.
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Motion and Differential Calculus
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Motion and Differential Calculus
The concept of a differential is all in the slope
of the tangent line at a point (time).
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Motion and Differential Calculus
Which graph is for an object slowing down and
coming to a stop? Which graph is for an object
moving with a constant velocity? Which graph is
for an object moving with a constantly increasing
velocity? Which graph is for an object slowing
down and then speeding up in the other direction?
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Motion and Differential Calculus
Which graph is for an object moving at a constant
velocity, then acceleration, and finally moving
with a constant velocity? Which graph is for an
object moving with a constant acceleration? Which
graph is for an object moving with a constantly
increasing acceleration? Which graph is for an
object that starts out accelerating and then
moves with a constant velocity?
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Motion and Differential Calculus
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Motion and Differential Calculus
How is v(t) related to x(t)? How is a(t) related
to v(t)?
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Motion and Differential Calculus
Rank in order, from largest to smallest, the
accelerations aA aC at points A C.
1) aA gt aB gt aC 2) aC gt aA gt aB 3) aC gt aB gt
aA 4) aB gt aA gt aC
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Motion and Differential Calculus
Rank in order, from largest to smallest, the
accelerations aA aC at points A C.
1) aA gt aB gt aC 2) aC gt aA gt aB 3) aC gt aB gt
aA 4) aB gt aA gt aC
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Motion and Differential Calculus
Which velocity-versus-time graph goes with this
position-versus-time graph on the left?
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Motion and Differential Calculus
Which velocity-versus-time graph goes with this
position-versus-time graph on the left?
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Motion and Differential Calculus
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Motion and Differential Calculus
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Motion and Differential Calculus
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Motion and Differential Calculus