Distance vs. Displacement,
Speed vs. Velocity,
Acceleration,
Free-fall,
Average vs. Instantaneous quantities,
Motion diagrams,
Motion graphs,
Kinematic formulas.
Distance
◦Tells “how far” an objectis from a given referencepoint or “how far” it hastraveled in a given time.
◦Is a scalar quantity whichmeans it has magnitudeonly
◦Is measured in lengthunits such as meters (m),centimeters (cm), feet (ft),inches (in), miles, etc.
Displacement
◦Tells “how far” and “whichway” an object moves.
◦Is distance in a givendirection
◦Is a vector quantitybecause it includesmagnitude and direction
◦The magnitude ismeasured in the sameunits as distance,direction is usuallymeasured as an angle.
d
“d” is the distance frompoint A to point B orfrom B to A
A
B
“d” is the distance from A to Band the arrow indicates thedirection of the displacement(from A to B).
d
B
A
Distance vs. DisplacementDistance vs. Displacement
start
end
2m
5m
5m
1m
1m
2m
3m
3m
Displacement
Distance :2+5+5+1+1+2 =16 m
Displacement:
@ 45° south of east
45°
S
W
N
E
Speed vs. VelocitySpeed vs. Velocity
Ex: speed = 60 mph
Ex: velocity =60 mph, N
Speed
◦Is the rate of change ofposition of an object
◦Tells “how fast” anobject is moving
◦Is a scalar quantitybecause it only includesmagnitude (size).
◦Measured in units ofdistance over time suchas mi/hr, km/hr, or m/s
Velocity
◦Is speed in a givendirection
◦Tells “how fast” and“which way”
◦Is a vector quantitybecause it includesmagnitude (speed) anddirection.
◦Magnitude is measuredin same units as speed.
The rate of change of velocity
◦How fast the speed changes
◦Measured in meters per second per second (m/s/s) ormeters per second squared ( )
◦A vector quantity (requires both magnitude and direction)
◦An object may accelerate (or decelerate) in three ways:
Speed up
Slow down
Change direction
◦If acceleration is…
…positive then it is in
the same direction as
the velocity causing velocity
to increase.
…negative then it is in the opposite
direction of the velocity causing velocity
to decrease (deceleration)
An object under the influence of only gravity is saidto be in “free-fall”
We assume no air resistance for any free-fallproblems…thus, the “only gravity” stipulation.
All objects fall at a constant acceleration… (9.81 m/s2downward near earth’s surface)…regardless of mass.(For quick calculations and estimates we can round to10 m/s/s)
This means that a falling object will gain 9.81 (or 10)m/s of speed every second that it falls.
Also…an object that is thrown up will slow down orlose 9.81 (or 10) m/s every second of its upwardmotion.
The velocity of the object at the tip-top of the path iszero, the acceleration is “g” the acceleration due togravity.
Average vs. Instantaneous velocityAverage vs. Instantaneous velocity
Average
◦Average velocity is thecalculated by dividingtotal distance traveledby total time
◦Constant velocity hasthe same value asaverage velocity
Instantaneous
◦Instantaneous velocity isthe velocity that anobject has at a specificinstant in time.
◦It is NOT the velocityover a time interval.
◦Initial velocity and finalvelocity are examples ofinstantaneous velocities.
A series of pictures illustrating the motion of theobject including displacement, velocity, andacceleration.
The rules:
◦4 images at equal time intervals…pay attention tospacing
◦Include and label velocity vectors with relative lengths torepresent relative speed on each image
◦Include and label a single acceleration vector
![C:\Users\Steph\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.IE5\QL9VNFJC\MCj04370990000[1].png](data/images/img16.png)
v
v
v
v
a=0
Example: Car moving to the right at constant velocity
The term “constant velocity” means that the car will cover equal distancesin equal time intervals…thus equal spacing. Also all velocity vectors are thesame length indicating the same speed. If there is no change in speed,there is no (zero) acceleration.
Distance
Time
faster
slower
The slope of the line on a distance-
time graph tells us about the speed.
Steeper slope means faster speed
Straight line means constant speed
For non-constant motion, the instantaneousspeed can be calculated by finding the slope ofthe tangent line at that point.
Δd
Δt
Distance
Time
Acceleration(increasing slope)
Distance
Time
Deceleration(decreasing slope)
Velocity
Time
The slope of the line on a velocity-
time graph tells us about the acceleration.
Steeper slope higher acceleration
Straight line means constant acceleration
For non-constant motion, the instantaneousacceleration can be calculated by finding theslope of the tangent line at that point.
Δv
Δt
velocity
Time
velocity
Time
Changing accelerations
Velocity
Time
10 sec
8 m/s
Area
The area under the curve of avelocity-time graph for aparticular time interval givesthe displacement of the objectduring that time interval.
The seconds cancelout and the units ofthe area are meters,therefore area is adisplacement.
acceleration
Time
Horizontal line means constant acceleration
We will not do any calculations with changingaccelerations, we assume all accelerations to be constant.
0
Positive constant acceleration
Negative constant acceleration
Zero acceleration (constant velocity)
Note:
The slope of ahorizontal line is zero.
The slope of a verticalline is undefined.
Interpreting graphs(constant motion)Interpreting graphs(constant motion)
time
time
time
distance
velocity
acceleration
Slope from this gives you this
Slope from this gives you this
The slope of the pink line isa lower positive constantvalue.
The slope of the blue line isa greater positive constantvalue
The slope of the green lineis a negative constantvalue.
A lower positive constantslope means a slowerpositive constant velocity(horizontal line).
A greater positive constantslope means a faster positiveconstant velocity (horizontalline).
A negative constant slopemeans a negative constantvelocity (horizontal line).
The slope of ahorizontal line is zero,so the acceleration forall three cases is zero.All three motions (pink,blue, and green) aregraphed along the timeaxis at acceleration = 0.
time
distance
time
velocity
time
acceleration
Slope from this gives you this
Slope from this gives you this
The slope of the red linestarts at a fairly low (flat)value and is increasing(gets steeper) steadily overtime.
The slope of the green linestarts at a higher value (it’ssteeper) and decreases(gets flatter) over time.
Increasing slopeindicates an increasingvelocity over time.
Decreasing slopeindicates a decreasingvelocity over time.
We will assume thechanges are takingplace at a steady rate.
Since the slope of the velocitygraph is a positive constantvalue we know that theacceleration is positive andconstant, therefore a horizontalline above the axis on theacceleration graph.
The slope on the velocity graphis negative and constant so theacceleration is a constantnegative value, therefore ahorizontal line below the axis.
Calculatingaveragevalues
Calculatinginstantaneousvalues
“free-fall” acceleration due to gravity
a=9.81m/s2, down
“at rest” not moving
v=0
“dropped” starts at rest and free-fall
vi=0 and a=9.81m/s2, down
“constant velocity” no acceleration
a=0
“stops” final velocity is zero
vf=0
These are the most common but be on thelookout for more.
