Download - A Summary of Motion
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A Summary of Motion
Measurements,
Graphs and Equations
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Scalars and Vectors Scalar quantities are measurements that have
no statement of direction.
Vector quantities are measurements that havea statement of direction.
Direction can be forward or backwards,
indicated by + or - , or it can be compasspoints such as N, S, E, or W. Up and down
are also directions
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Position Position is the location of an object based on a
reference point. Often, though not always, the
reference point is assigned a zero value. A reference point does not have to be zero, it
can be any point the author of a problem
decides it should be. The starting point in a motion problem does
not have to be the reference point.
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Displacement Displacement is a measure of an objects
change in position.
Displacement is usually measured in a straightline from the start position to the end position
of the motion.
Displacement has a direction associated withit. This could be forward vs reverse, or north
vs south, or east vs west, or up vs down.
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Speed Speed is a statement about how fast an object is
traveling.
Speed measures the rate of change between distance
and time. Speed has no statement of direction.
Speed is found by dividing the total distance traveledby an object by the time interval during which the
object moved. Speed is the magnitude of an objects velocity
Speed has a number and a unit; i.e. 5 m/s
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Velocity Velocity is a statement about how fast an object is
going plus the direction it is going.
Velocity measures the rate of change between
displacement and time. Velocity has a statement of direction.
Velocity is found by dividing the displacement of anobject by the time interval during which the object
moved. Velocitys magnitude is speed
Velocity has a number, a unit, and direction; i.e. 5m/s, E
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Acceleration Acceleration is a statement about how fast an
objects velocity changes.
Acceleration measures the rate of change between
velocity and time.
Acceleration has a statement of direction.
Acceleration is found by dividing the change invelocity of an object by the time interval duringwhich the velocity changed.
Acceleration has a number, a unit, and direction; i.e.9.8 m/s^2, N
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Constant velocity (uniform motion) Constant velocity is a
situation where an
object moves along
with a constant change
in its position.
On the right youll see
a typical position-timegraph where the
velocity is constant.
Position vs Time
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Constant Velocity (uniform motion) Constant velocity is a
situation where an
object moves along
with a constant change
in its position.
On the right youll see
a typical velocity-timegraph where the
velocity is constant
Velocity vs Time
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Uniform (constant) Acceleration Uniform or constant
acceleration is asituation where an
object moves alongwith a constant changein its velocity.
On the right youll see
a typical position-timegraph where theacceleration is constant
Position vs Time
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Uniform (constant) Acceleration
Uniform or constantacceleration is asituation where an
object moves alongwith a constant changein its velocity.
On the right youll see
a typical velocity-timegraph where theacceleration is constant
Velocity vs Time
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Falling Bodies and Acceleration
According to the Law of Gravity, all objects
fall with the same rate of acceleration when
they are in free fall. Free fall is a situation where air friction has
no effect on the falling body.
On earth (only) the average rate ofdownwards acceleration g is 9.8 m/s^2
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Summary:
We have looked at three generic scenarios.
1. Constant velocity
2. Acceleration in a horizontal direction 3. Acceleration in a vertical direction; free fall
For further review it is strongly recommended
that you go to your text references and read,study, and take notes on the example and thepractice problems in your textbook.
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Acceleration due to Gravity
Uniform acceleration
of gravity is a situation
where an object falls
along with a constant
change in its velocity.
On the right youll see
a typical position-timegraph where an object
accelerates downwards.
Position vs Time
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Acceleration due to Gravity
Uniform acceleration
of gravity is a situation
where an object falls
along with a constant
change in its velocity
On the right youll see
a typical velocity-timegraph where an object
accelerates downwards.
Velocity vs Time
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Time; clock time and time interval
Time can be thought of in one of two ways. Itcan be an exact time as in What time is itright now? or it can represent a period oftime often referred to as the duration of anevent.
t or Clock time is what it says on a clock, etc.
/\t = t(f)t(i) is the difference between twoclock times and is often referred to as theduration of an event.
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Distance and Speed
Distance or what is often called total distance
is not the same as displacement. It is simply
the total of all of the distances an objecttravels in a time interval
Speed is simply equal to the total of all of the
distances divided by the time interval. Equation: Speed = d(total) / /\t
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Equations for Constant velocity
Constant velocity: velocity that remains thesame during the time interval an ojectsmotion is being studied or observed.
/\d = d(f)d(i); often d(i) = 0 m, km, mi, etc.,so /\d is simply d(f) or d(total)
V(ave) = /\d / /\t
/\d = V(ave) * /\t
/\t = /\d / V(ave)
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Equations for Uniform Acceleration
Uniform acceleration: The situation where thevelocity continuously changes by the same amountof velocity each second, thus causing position tochange by an ever increasing amounts per unit oftime (i.e. per second)
a(ave) = /\v / /\t; where /\v = v(f)v(i)
d(f) = d(i) + 0.5 [{vi + vf} / 2] /\t
d(f) = v(i) /\t + 0.5 a /\t^2 v(f) = v(i) + a t
v(f)^2 = v(i)^2 + 2 a /\d
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Equations for Uniform Acceleration
during free fall. (g = a = 9.8 m/s^2)
Uniform acceleration: The situation where thevelocity continuously changes by the same amountof velocity each second, thus causing position tochange by an ever increasing amounts per unit oftime (i.e. per second)
g(ave) = /\v / /\t; where /\v = v(f)v(i)
d(f) = d(i) + 0.5 [{v(i) + v(f)} / 2] /\t
d(f) = v(i) /\t + 0.5 g /\t^2 v(f) = v(i) + g /\t
vf^2 = vi^2 + 2 g /\d