The Equations of Motion in 1D with Acceleration Constant

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The Equations of Motion in 1D with Acceleration
Constant
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The Equations of Motion in 1D with Acceleration
Constant
or
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The Equations of Motion in 1D with Acceleration
Constant
or
The change in position equals the (average)
velocity times the time of travel.
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The Equations of Motion in 1D with Acceleration
Constant
slope vx
?x
or
(y m x b)
?t
The change in position equals the (average)
velocity times the time of travel.
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xf
slope vx
or
xi
ti
tf
Your final position (xf) depends on where you
start (xi) and the additional distance you travel
at velocity vx over time interval (tf ti).
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A particular velocity
xf
slope vx
or
xi
ti
tf
Your final position (xf) depends on where you
start (xi) and the additional distance you travel
at velocity vx over time interval (tf ti).
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x
Adding together travel at different velocities
during different time intervals produces a more
general graph of position over time.
positive slope positive velocity
t
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x
Adding together travel at different velocities
during different time intervals produces a more
general graph of position over time.
negative slope negative velocity
positive slope positive velocity
t
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x
Adding together travel at different velocities
during different time intervals produces a more
general graph of position over time.
negative slope negative velocity
zero slope zero velocity
positive slope positive velocity
t
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Positive velocity means moving in the x
direction (toward more positive values of x)
negative velocity means moving in the x
direction (toward more negative values of x).
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Positive velocity means moving in the x
direction (toward more positive values of x)
negative velocity means moving in the x
direction (toward more negative values of x.
x (m)
3
0
t (s)
0
3
You walk at 1 m/s for 3 seconds, starting at x
0 m
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Positive velocity means moving in the x
direction (toward more positive values of x)
negative velocity means moving in the x
direction (toward more negative values of x.
x (m)
3
0
t (s)
0
3
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You walk at 1 m/s for 3 seconds, starting at x
0 m you stop for 2 s
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Positive velocity means moving in the x
direction (toward more positive values of x)
negative velocity means moving in the x
direction (toward more negative values of x.
x (m)
3
0
t (s)
0
3
5
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You walk at 1 m/s for 3 seconds, starting at x
0 m you stop for 2 s then you turn around and
run at -3 m/s for 1 s.
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Positive velocity means moving in the x
direction (toward more positive values of x)
negative velocity means moving in the x
direction (toward more negative values of x.
x (m)
3
0
t (s)
0
3
5
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You walk at 1 m/s for 3 seconds, starting at x
0 m you stop for 2 s then you turn around and
run at -3 m/s for 1 s. What happens if you
continue at -3 m/s for another 1 s?
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You end up at location -3 m (3 meters in the x
direction from where you started at x 0 m).
x (m)
3
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0
t (s)
0
3
5
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-3
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Good for finding position if velocity is constant
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Good for finding position if velocity is constant
or if it is constant over periods of time
x
t
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Good for finding position if velocity is constant
or if it is constant over periods of time
x
The graph of velocity as a function of time (for
the graph at right)
t
vx
t
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Good for finding position if velocity is constant
or if it is constant over periods of time
x
The graph of velocity as a function of time (for
the graph at right)
t
vx
t
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Good for finding position if velocity is constant
or if it is constant over periods of time
x
The graph of velocity as a function of time (for
the graph at right)
t
vx
t
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Good for finding position if velocity is constant
or if it is constant over periods of time
x
The graph of velocity as a function of time (for
the graph at right)
t
vx
t
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What happens when the velocity changes
continuously?
vx
t
How does position (x) change with time?
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What happens when the velocity changes
continuously?
vx
t
How does position (x) change with time? Changing
velocity means that acceleration is non-zero.
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What happens when the velocity changes
continuously?
vx
t
How does position (x) change with time? Changing
velocity means that acceleration is non-zero.
or
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What happens when the velocity changes
continuously?
vx
t
How does position (x) change with time? Changing
velocity means that acceleration is non-zero.
We will assume that ax is non-zero but constant
or
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Combining the position and velocity equations
gives an equation for position, assuming constant
acceleration
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Combining the position and velocity equations
gives an equation for position, assuming constant
acceleration
Rewriting average velocity (using geometry) as ½
(vf vi) gives another equation that relates
position, velocity and acceleration (without
explicit time dependence)
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Combining the position and velocity equations
gives an equation for position, assuming constant
acceleration
Rewriting average velocity (using geometry) as ½
(vf vi) gives another equation that relates
position, velocity and acceleration (without
explicit time dependence)
This equation is useful when you know 3 out of
the 4 variables (above) AND you dont know ?t.
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Motion with constant acceleration
equationssummary