a summary of motion

7/28/2019 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.


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.


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.


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.


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


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

a summary of motion

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