6. Can an object
have a constant
speed and a
varying velocity at
the same time?
Explain.
Chapter 2 Linear Motion
Speed
 Velocity
 Acceleration
 Free Fall
 Graphing

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
Rate is essential to describing motion
Quantity/time = rate
› Tells how fast something happens
› How much something changes
› Speed, velocity and acceleration are all
rates…
› What is linear motion?
 Motion along a straight line path
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

When we discuss the
When sitting on a chair, your
motion of something,
speed is zero relative to the
we describe motion
Earth but 30 km/s relative to
the sun
relative to something
else.
Unless stated otherwise,
when we discuss the
motion of objects in our
environment we mean
relative to the surface A book at rest, relative to
of the Earth.
the table it lies on, is
moving about 30 km/s
relative to the sun
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
As we stand still we are hurtling through
space
› A train is leaving the station or is the station
leaving the train?
› A car in the Indy 500 travels 500 miles but
ends up at the same point
› On the school bus traveling 30 mph you
throw a ball to a classmate, how fast is the
ball moving?
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




Speed is a measure of how fast something
moves.
Speed is a scalar quantity, meaning it does
NOT include direction
Two units of measurement are necessary for
describing speed: units of distance and time
Speed is defined as the distance covered per
unit time: speed = distance/time
Units for measuring speed: km/h, mi/h (mph),
m/s
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
Speed is the measure of how fast
something moves, a unit of distance
divided by a unit of time. We think of it in
two ways
› Instantaneous speed
› Average speed
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The speed at any instant is the
instantaneous speed.
 The speed registered by an automobile
speedometer is the instantaneous
speed.
 Not the same as Average speed…

8
You are in a car heading downtown, as
you can see from the speedometer your
speed is 40 mi/h
 Downtown is 10 miles away at this speed
how long will it take you?
 Speed= Distance/time

› solve for time T=D/S
› T=10m/40mi.hr =
› .25 hour (15 minutes)
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Average speed is the whole distance
covered divided by the total time of travel.
 General definition:

› Average speed = total distance covered/time
interval

Distinguish between instantaneous speed
and average speed:
› On most trips, we experience a variety of
speeds, so the average speed and
instantaneous speed are often quite different.
› Is a fine for speeding based on ones average
speed or instantaneous speed?
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
Example 1: If we travel 320 km in 4 hours, what is
our average speed? If we drive at this average
speed for 5 hours, how far will we go?
› List the known and unknowns. Then start with the
formula for average speed
› Savg=Total distance/ Time
› Answer: Savg = 320 km/4 h = 80 km/h.
› d = Savg x time = 80 km/h x 5 h = 400 km.

Now you try: During a race, Andra runs with an
average speed of 6.02 m/s, What distance will she
cover in 137s?
› Savg = 6.02 m/s, t= 137s, d=?
› d = Savg x time 6.2x137
› 825 m
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

Velocity is speed in a given
direction; when we describe speed
and direction of motion, we are
describing velocity.
Velocity = speed and direction;
velocity is a “vector quantity”.,
meaning it has speed AND
direction
› If a car travels at 60 km/h we have
defined it’s speed, but if we say its
traveling at 60 km/h to the north, we
have defined it’s velocity

Constant velocity = going in a
straight link at the same speed
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
What is acceleration?
› It’s NOT just an increase in speed!

Acceleration tells you how fast (the rate) velocity
changes:
› Acceleration = change in velocity/time interval
› Acceleration is not the total change in velocity; it is the time
rate of change!


When we accelerate in a car from stop to 60 km/h in
5 seconds, we have changed our speed– this is
acceleration
The same applies when we are in a car that slowsthis is called negative acceleration or Deceleration
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


You feel the effects of acceleration as your body
tends to move outward toward the outside of the
curve.
You round the curve at a constant speed, but
YOUR velocity is not constant- your direction is
changing every instant- you are accelerating
Acceleration= change in velocity/time interval
› This is measured in m/s2
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Distance: how far something travels
 Displacement: how far out of place an
object is; the object’s overall change in
position (has magnitude and direction)

› Displacement is NOT always equal to
distance traveled
› Can be positive or negative

SI (Systeme International) unit for
distance and displacement is meter (m)
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To test your understanding of this distinction, consider
the motion depicted in the diagram below.
 A physics teacher walks 4 meters East, 2 meters South, 4
meters West, and finally 2 meters North.

Total distance is 12 meters
 Displacement is 0 meters- she is right back where she
started
 Displacement worksheet

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
Benjamin watches a thunderstorm from his
apartment window. He sees the flash of lightning
bolt and begins counting the seconds until he
hears the clap of thunder 10 s later. Assume that
the speed of sound in air is 340 m/s. How far away
was the lightning bolt in m?.
› What are the givens? Find Vavg, ∆t and ∆d
 Vavg = 340 m/s
Vavg= ∆t
 ∆t= 10.0 s
∆d
 ∆d=?
 ∆d= 3400m
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
The slowest animal ever discovered was a
crab found in the Red Sea. It traveled with
an average speed of 5.70 km/y. How long
would it take this crab to travel 100 km?
› What are the givens?
 Vavg = 5.70 km/y
 ∆t= ?
 ∆d=100 km
100km
570 km/y = 17.5 y
∆t = ∆d
Vavg
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
Galileo’s findings:
› A ball rolls down an inclined plane with unchanging
acceleration.
› The greater the slope of the incline, the greater the
acceleration of the ball.
› If released from rest, the instantaneous speed of the
ball at any given time = acceleration x time.
› What is its acceleration if the incline is vertical?
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
Depends on:
› Acceleration
› initial velocity
› Time

Displacement = ∆x
› ∆x= ½ (Vi +Vf) ∆t Example 2 c
› Vf=Vi +a ∆t
› ∆x= Vi ∆t + ½a(∆t) Example 2D
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
A racing car reaches a speed of 42 m/s.
It then begins a uniform negative
acceleration, using its parachute and
braking system, and comes to rest 5.5 s
later. Find how far the car moves while
stopping.
∆x= ½ (Vi +Vf) ∆t
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
A plane starting at rest at one end of a runway
undergoes a uniform acceleration of 4.8 m/s2
for 15s before takeoff. What is its speed at
takeoff? How long must the runway be for the
plane to be able to take off?
∆x= Vi ∆t + ½a(∆t)2
Vf=Vi +a ∆t
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A person pushing a stroller starts from
rest, uniformly accelerating at a rate of
0.500 m/s2. What is the velocity of the
stroller after it has traveled 4.75 m?
 Work together to find formula and
answer.

23
If a rock is dropped off the side of a
cliff we would expect it to fall and
during the fall we would expect it to
accelerate.
 If there was no air resistance its
speed would increase by
approximately 10 m/s every
second. So after 5 seconds, it’s
speed would be 50 m/s
 Free fall: motion of an object falling
with a constant acceleration

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

Freely falling bodies undergo
constant acceleration
If we are on a cliff on the Moon,
therefore there is no atmosphere – a
vacuum and we dropped a feather
and the rock at the same time what
would happen?
› They would fall together with the same
acceleration.


On Earth, we have air resistance, so
things change!
Would you rather jump out of a plane
with a parachute or not? Why?
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Free-fall acceleration ‘g’=9.81 m/s2
 Downward acceleration is negative
so
a= -9.81 m/s2
 What goes up must come down
› Objects thrown in the air have a
downward acceleration as soon as they
are released.
› At the top of the path, the balls velocity
= 0.
› Acceleration however is -9.81 m/s2 at
every moment in both directions
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Sample 2 F
 Jason hits a volleyball so that it moves with
a initial velocity of 6.0 m/s straight upward.
If the volleyball starts from 2.0 m above the
floor, how long will it be in the air before it
strikes the floor? Assume that Jason is the
past player to touch the ball before it hits
the floor.
Vf2=Vi2+2a∆y or Vf=Vi + a∆t

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Used to visually describe relationships
between something such as distance
and time
 the specific features of the motion of
objects are demonstrated by the shape
and the slope of the lines on a position
vs. time graph

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
To begin, consider a car moving with a
constant, rightward (+) velocity - say of
+10 m/s.
PHY 1071
Dr. Jie Zou
29
http://www.physicsclassroom.com/
class/1dkin/u1l3a.cfm
PHY 1071
Dr. Jie Zou
30