Kinematics
Chapter 2
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Motion in One Dimension
Describes motion while ignoring the
agents that caused the motion
For now, will consider motion in one
dimension
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Position
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Defined in terms of a
frame of reference
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A particle is a point-like object, has mass
but infinitesimal size
Position-Time Graph
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One dimensional, so
generally the x- or yaxis
The object’s position
is its location with
respect to the frame
of reference
Along a straight line
Will use the particle model
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The position-time
graph shows the
motion of the
particle (car)
The smooth curve is
a guess as to what
happened between
the data points
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Displacement
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Defined as the change in position
during some time interval
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Represented as Δx
Δx = xf - xi
SSI units are meters (m) Δx can be positive
or negative
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The average velocity is rate at which
the displacement occurs
Vector quantities need both magnitude (size
or numerical value) and direction to
completely describe them
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Different than distance – the length of a
path followed by a particle
Average Velocity
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Vectors and Scalars
Scalar quantities are completely described by
magnitude only
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The dimensions are length / time [L/T]
The SI units are m/s
Is also the slope of the line in the
position – time graph
Ex: distance
Average Speed
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Speed is a scalar quantity
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Ex: displacement
Will use + and – signs to indicate vector directions
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same units as velocity
total distance / total time
The average speed is not (necessarily)
the magnitude of the average velocity
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Ch 2: Problem 4
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A particle moves according to the
equation x = 10 t2 where x is in meters
and t is in seconds.
(a) Find the average velocity for the
time interval from 2.00 s to 3.00 s.
Instantaneous Velocity,
equations
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The general equation for instantaneous
velocity is
Instantaneous Velocity
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Instantaneous Velocity, graph
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The instantaneous velocity can be
positive, negative, or zero
The limit of the average velocity as the
time interval becomes infinitesimally
short, or as the time interval
approaches zero
The instantaneous velocity indicates
what is happening at every point of time
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The instantaneous
velocity is the slope
of the line tangent to
the x vs. t curve
This would be the
green line
The blue lines show
that as Δt gets
smaller, they
approach the green
line
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Instantaneous Speed
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The instantaneous speed is the
magnitude of the instantaneous velocity
Remember that the average speed is
not the magnitude of the average
velocity
Average Acceleration
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Acceleration is the rate of change of the
velocity
Dimensions are L/T2
SI units are m/s2
Ch 2: Problem 8
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A position-time graph for a
particle moving along the x
axis is shown.
(a) Find the average velocity
in the time interval t=1.50 s to
t=4.00 s.
(b) Determine the
instantaneous velocity at
t=2.00 s by measuring the
slope of the tangent line
shown in the graph.
(c) At what value of t is the
velocity zero?
Instantaneous Acceleration
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The instantaneous acceleration is the limit of
the average acceleration as Δt approaches 0
Acceleration is curvature of position-time
graph
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Instantaneous Acceleration -graph
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The slope of the
velocity vs. time graph
is the acceleration
The green line
represents the
instantaneous
acceleration
The blue line is the
average acceleration
Acceleration and Velocity, 1
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When an object’s velocity and
acceleration are in the same direction,
the object is speeding up
When an object’s velocity and
acceleration are in the opposite
direction, the object is slowing down
Ch 2: Probem 11
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A 50.0-g superball traveling at 25.0 m/s
bounces off a brick wall and rebounds
at 22.0 m/s. A high-speed camera
records this event. If the ball is in
contact with the wall for 3.50 ms, what
is the magnitude of the average
acceleration during this time interval?
Acceleration and Velocity, 2
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The car is moving with constant positive velocity
(shown by red arrows maintaining the same size)
Acceleration equals zero
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Acceleration and Velocity, 3
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Velocity and acceleration are in the same direction
Acceleration is uniform (blue arrows maintain the
same length)
Velocity is increasing (red arrows are getting longer)
This shows positive acceleration and positive velocity
Kinematic Equations -summary
Acceleration and Velocity, 4
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Acceleration and velocity are in opposite directions
Acceleration is uniform (blue arrows maintain the
same length)
Velocity is decreasing (red arrows are getting shorter)
Positive velocity and negative acceleration
Ch 2: Problem 19
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Jules Verne in 1865 suggested sending
people to the Moon by firing a space capsule
from a 220-m-long cannon with a launch
speed of 10.97 km/s. What would have beent
he unrealistically large acceleration
experienced by the space travelers during
launch?
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Ch 2: Problem 20
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A truck covers 40.0 m in 8.50 s while
smoothly slowing down to a final speed
of 2.80 m/s. (a) Find its original speed.
(b) Find its acceleration.
Graphical Look at Motion –
displacement – time curve
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The slope of the
curve is the velocity
The curved line
indicates the velocity
is changing
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Graphical Look at Motion –
velocity – time curve
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The slope gives the
acceleration
The straight line
indicates a constant
acceleration
Therefore, there is
an acceleration
Graphical Look at Motion –
acceleration – time curve
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The zero slope
indicates a constant
acceleration
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Ch 2: Problem 15
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A particle moves along the x axis
according to the equation
x = 2.00 + 3.00 t - 1.00 t2
where x is in meters and t is in seconds.
At t=3.00 s, find
(a) the position of a particle,
(b) its velocity,
(c) its acceleration.
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