• Kinematics is the study of motion
• Motion is relative
PHYS 1114: College Physics 1
Lecture 3:
Kinematics of Distance, Speed, & Velocity
– Motion is always measured relative to a
reference frame.
– The reference frame is what is considered to
be at rest (not moving).
– The reference frame is generally assumed to
be the earth
• EXAMPLE:
Professor'Kenny'L.'Tapp
– If a car traveling at 30 m/s passes a truck
going 10 m/s, the car is said to be going 20 m/
s relative to the truck. This holds the truck
(instead of the earth) as a frame of reference.
Definitions
Examples: Linear
• Instantaneous
– Value at a point, at an instant
• 2:01
• Speedometer
• Interval
– Difference between two points
– Represented by Δ
• Time length of class
Linear Motion
• Describing race distances:
– 100 m sprint
– Indy 500 auto race
– 4000 km Tour de France
• Characterizing performance
– Shot put distance
– Long jump distance
– Pole vault height
• Typical units: ___________________
Vectors(and(Scalars
Most%all%Physics%quan00es%can%be%described%as%
either%a%vector%or%scalar.
• A(SCALAR(is(a(quan5ty(that(takes(one(piece(of(
informa5on(to(describe.
• A(VECTOR(is(a(quan5ty(that(takes(two(pieces(
of(informa5on(to(describe.
Distance(vs.(Displacement
• Distance
– Scalar
– Always(posi5ve
– Measured(in(meters((m)
– (Absolute(value(of(the(path(length(traveled
Distance(vs.(Displacement
• Displacement(
– Vector
– May(be(posi5ve(or(nega5ve
– Measured(in(meters((m)
– The(difference(between(the(final(posi5on(and(the(
ini5al(posi5on
d=x2Mx1
Distance
Distance is the path length traveled from one
location to another. It will vary depending on the
path.
Distance is a scalar quantity—it is described
only by a magnitude.
Displacement
• Displacement(can(be(posi5ve(or(nega5ve
• These(indicate(direc5on(of(mo5on
• Point(the(direc5on(of(mo5on
• Can(you(be(on(the(+x(axis(and(have(a(nega5ve(
displacement?
– Indicated(with(a(vector(arrow(poin5ng(from(ini5al(
to(final(posi5on
Distance(vs.(Displacement
Displacement is a vector that points from the
initial position to the final position of an object.
Quick Question 1
• A race car traveled at 50.0 m/s for 4 hours.
How much distance has been covered in
this time?
Speed(vs.(Velocity
Velocity(
• Speed
• Velocity
– Scalar
– Always(posi5ve
– Measure(in(meters/second((m/s)
– Average(speed=( distance(traveled
( (
(
(
(
– Vector
– Can(be(pos5ve(or(nega5ve
– (Measured(in(m/s(also
• Average(Velocity=( Displacement
( ( ( ( ( ( ( ( ( Time
• Instantaneous(velocity(is(velocity(at(a(moment(
in(5me
(((((((((((total(5me
Quick Question 2
Graphical Representation of Motion
Velocity of the Paper Airplane
• It is also useful to graph position versus
time.
• We will make the decision that when t=0,
our position, x, will be 0.
• Since the car is moving with constant
velocity, we can easily calculate how far
the car will have traveled in 1s, 2s, 3s, etc.
Determine the final velocity of your paper airplane
using displacement and time.
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Graphical Representation of Motion
Graphical Representation of Motion
Plotting this gives us the following graph:
• Consider a car traveling at a constant
velocity of 10 m/s. If we were to draw a
graph of velocity versus time, it would look
like this:
Slope of this line = Δx/ Δt
Graphical Representation of Motion
This object’s velocity
is not uniform. Does it
ever change direction,
or is it just slowing
down and speeding
up?
Acceleration
Kinematic Profile
• Sometimes νelocity (v) over relatively long
time (t) is not very informative...
– reflects need for a "kinematic profile" for more
detailed information about performance.
During a Soccer Kick:
instantaneous estimates
of performance gives
more detail about
performance.
Acceleration
Acceleration means that the speed of an object
is changing, or its direction is, or both.
Acceleration may result in an
object either speeding up or
slowing down (or simply
changing its direction).
Accelera5on(
• Accelera5on(
– Vector
– Can(be(posi5ve(or(nega5ve
– Unit(of(m/s2
Acceleration is the
rate at which
velocity changes.
• Ave.(accelera5on=(( change(in(velocity
( ( ( ( ( ( ( ( change(in(5me
Acceleration
If the acceleration is constant, we can find the
velocity as a function of time:
Quick(Ques5on(3:
• A Cheetah accelerates uniformly from rest
to 22 m/s in 2.0 s. What is its
acceleration?
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Quick(Ques5on(4:
Quick(Ques5on(5:
• An automobile initially traveling at 30 m/s,
is braked to a stop in 15 s. Find the
average acceleration of the car.
• A motorcycle traveling at 40 m/s is given
an average acceleration of 4 m/s2 for 10 s.
Find the final velocity.
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Example: Distance
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Example: Displacement
Example: Speed
Example: Acceleration
Example: Velocity