Motion in One Dimension – Part 1
POSITION & DISPLACEMENT
KINEMATICS IN ONE DIMENSION
Kinematics: From the Greek kinema, meaning “motion.” Kinematics is the description of
motion. This is where the word “cinema” comes from, because they are moving pictures
(that’s why they are called movies).
Motion in One Dimension – Part 1 > Position & Displacement
POSITION & DISPLACEMENT
A
B
Position: describes where the object is
relative to the origin. This can be
positive or negative.
Displacement: Change between
two positions. This can be positive
or negative.
ending
position
C
Δx = xf ̶ xi
displacement
Motion in One Dimension – Part 1 > Position & Displacement
starting
position
POSITION & DISPLACEMENT
What is the displacement if the person starts in the position shown in A and then ends
in the position shown in B?
A
B
Motion in One Dimension – Part 1 > Position & Displacement
POSITION & DISPLACEMENT
What if he starts at B and ends at A?
B
A
Motion in One Dimension – Part 1 > Position & Displacement
POSITION VS. TIME
A position vs. time graph shows where an object is at each time.
I walk at a constant speed across
the classroom, stop, hang out and
then run back. What does the
position vs. time graph look like?
Motion in One Dimension – Part 1 > Position & Displacement
END OF SECTION
Motion in One Dimension – Part 1
VELOCITY
POSITION VS. TIME
From last lecture:
A position vs. time graph shows
where an object is at each time.
I walk at a constant speed across the
classroom, stop, hang out and then
run back. What does the position vs.
time graph look like?
Motion in One Dimension – Part 1 > Velocity
AVERAGE VELOCITY
The average velocity is the displacement divided by the time interval.
What is the average velocity for: A, B, C?
Motion in One Dimension – Part 1 > Velocity
v=
Δx
Δt
AVERAGE VELOCITY
The average velocity is the displacement divided by the time interval.
v=
What is the average
velocity for the whole trip:
A
a.
1.8m/s
B
b.
0.6m/s
C
c.
0.3m/s
d.
None of the above
D
Motion in One Dimension – Part 1 > Velocity
Δx
Δt
AVERAGE VELOCITY
If the position vs. time graph is the blue line, what
is the average velocity for: A, B, C?
Motion in One Dimension – Part 1 > Velocity
AVERAGE VELOCITY
The average velocity, in some time intervals, is the slope of the line connecting those points on
the position vs. time graph.
v=
Δx
Δt
Adapted from: R. A. Serway and J. W. Jewett: Physics for Scientists and Engineers Vol. 1
Motion in One Dimension – Part 1 > Velocity
INSTANTANEOUS VELOCITY
The instantaneous velocity is the velocity at an instant in time. It is equal to the slope of
the tangent to the position vs. time graph at that point.
To find the velocity at
a single point, take the
limit of the average
velocity as Δt 0
Adapted from: R. A. Serway and J. W. Jewett: Physics for Scientists and Engineers Vol. 1
Motion in One Dimension – Part 1 > Velocity
INSTANTANEOUS VELOCITY
The slopes of 3 tangent lines give the instantaneous velocity at 3 different times.
Motion in One Dimension – Part 1 > Velocity
QUESTION 1
The figure shows position vs. time graphs for four objects.
Which starts slowly and then speeds up?
A
Motion in One Dimension – Part 1 > Velocity
B
C
D
VELOCITY VS. TIME
A velocity vs. time graph shows the
velocity as a function of time.
Motion in One Dimension – Part 1 > Velocity
Draw a velocity vs. time graph for the
animation showing the man move
across a room and back.
END OF SECTION
Motion in One Dimension – Part 1
ACCELERATION
AVERAGE ACCELERATION
Similar to average velocity, the average acceleration is the change in
velocity over the time.
a=
Δv
Δt
The instantaneous acceleration is the acceleration at an instant in time.
It is equal to the slope of the tangent to the velocity vs. time graph at
that point.
For now, we will stick to “constant” accelerations. “Constant” because
we may have more than one constant acceleration in a problem.
Motion in One Dimension – Part 1 > Acceleration
DEMO
Draw the graphs.
Motion in One Dimension – Part 1 > Acceleration
DEMO
Acceleration and velocity in opposite direction slowing down
Acceleration and velocity in the same direction speeding up
Motion in One Dimension – Part 1 > Acceleration
TURNING POINTS
When position vs. time graphs have local maximum or minimum values, this is a turning point.
At the maximum and minimum points, the velocity is ZERO. It has to stop to turn around.
The fact that the velocity is zero does not mean the acceleration is zero!
Motion in One Dimension – Part 1 > Acceleration
END OF SECTION
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