Motion in a Straight Line Position Velocity Acceleration.
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Transcript of Motion in a Straight Line Position Velocity Acceleration.
Motion in a Straight Motion in a Straight LineLine
PositionVelocity
Acceleration
Name Some Things That Name Some Things That MoveMove
Vehicles – cars, planes, etc. Animals – birds fly…fish swim…
people walk Molecules – vibrational, rotational
and translational motion The Earth, the moon, the sun, the
Galaxy…the universe …everything moves…maybe…
So…then, what is motion?
Motion is common to everything in the universe.
That is why it is the beginning of the study of physics.
Motion is described by three criteria: position, velocity and
acceleration.
POSITIONPOSITION
Must be defined relative to a reference point.
Must be defined using both magnitude and direction.
Displacement and Displacement and DistanceDistance
A objects displacement is defined as the separation between an object and a reference point.
It must be defined by magnitude and direction.
… and Distance?
Distance is simply the separation between any two points.
It is defined simply by magnitude.
Scalars and VectorsScalars and Vectors
What is a Scalar?What is a Scalar?
A scalar is a quantity that is described only by magnitude…such as distance.
The distance from Gainesville to Bronson is 22 miles.
What Is a Vector?What Is a Vector?
A vector is a quantity that must be described by magnitude and direction.
The displacement between Gainesville and Bronson is 22 miles at 32 degrees south of west.
Speed and VelocitySpeed and Velocity
The relationship between motion and
time.
SpeedSpeed
Speed is defined as the distance traveled per unit time.
It is a scalar quantity.
It units are meters per second (m/s).
t
ds
VelocityVelocity
Velocity is displacement per unit time.
It is a vector quantity.
Its units are meters per second (m/s).
t
dv
if
if
tt
dd
t
dv
More VelocityMore Velocity
It is defined relative to a reference point.
Velocity describes both speed and direction.
Depending on your direction, it can be negative or positive.
Now Remember This
Velocity is a vector quantity. Speed is a scalar quantity. Displacement is a vector
quantity. Distance is a scalar quantity.
DefinitionsDefinitions
Average Velocity
Instantaneous Velocity
Relative Velocity
AccelerationAcceleration
Consider an airplane taking off. As it goes down the runway it
increases its speed until it is going fast enough to
“lift off” the ground.
Son of AccelerationSon of Acceleration
The increase of velocity per unit time is called acceleration.
It is the rate of change of velocity.
Its units are meters per second squared (m/s^2).
Average Average AccelerationAcceleration
Average acceleration is the change in velocity divided by
the change in time.
t
vv
t
va if
…and some notes… Acceleration
is a vector. It can be
positive or negative.
At rest means initial time is zero.
When velocity is constant, acceleration is zero.
When velocity increases at a constant rate, acceleration is uniform.
The Motion The Motion EquationsEquations
2if
if
if
vvv
atvvt
vva
tvv
d
tvd
if
2
Displacement & Acceleration
By factoring out final velocity, we can get displacement in terms of initial velocity and uniform acceleration.
22
1 attvd i
……and what if you don’t and what if you don’t have time?have time?
Let’s factor time out of the equation and see what we get…
advv if 222
In SummationIn Summation
Now we have equations that will enable us to
solve for time, velocity, displacement and acceleration for
horizontal straight line motion.
……but wait a but wait a minute…minute…
What if it’s vertical straight line motion…
say, like a rocket going up at Cape Canaveral?!?
It’s really quite It’s really quite simplesimple
When you are traveling in a vertical direction, acceleration is always the same.
It is the acceleration of gravity, g, which always has the same value.
GRAVITYGRAVITY
2/80.9 smg
Vertical Motion
For vertical motion problems, simply substitute g for a in
any of the straight-line motion equations.