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1

Motion
Physics deals with quantities that can be measured
...
As you proceed through your study of physics, you will find that
every one of the measurable quantities that is discussed can be specified in terms
of only four basic dimensions: mass, length, time, and electric charge
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OBJECTIVES
After completing this chapter, you will be able to
• define speed;
• calculate speed, distance, or time, given the other two values;
• calculate acceleration, given initial and final velocities and the elapsed time;
• use a motion diagram to model the motion of an object;
• state the value of the acceleration of gravity;
• given an initial velocity, calculate the distance an object will fall in a given time;
• differentiate between speed and velocity;
• distinguish between scalar and vector quantities, giving an example of each;
• use the graphical method to add vectors;
• identify and classify (as to acceleration and velocity) each of the two components of projectile motion
...
Thus, if
you travel 12 miles in 3 hours, the average speed is 4 mi/hr (mi/hr or mph)
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It includes such units as inches, feet, and pounds
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*

1

2  BASIC PHYSICS

(a) If an elephant runs for half an hour at a speed of 6 mi/hr, what distance does
it cover? ______________________
(b) A box is on a conveyor belt
...
_____________________ 
Answers: (a) 3 
miles; (b) 1
...
For an object that moves with constant speed, the defining equation
for speed is:


v avg

d
t

Here v is the speed and d is the distance the object travels after time t
has elapsed
...
However, if the speed of the object changes while
moving, the above equation gives us just the object’s average speed
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That doesn’t mean your speed was 24 mi/hr for the entire trip
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An average speed doesn’t tell us how an object is moving at any
particular instant
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(a) What is the average speed of a car that covers 250 miles in 5 hours?
_________________________
(b) What is the average speed a plane flying 2,600 miles from New York City to
Los Angeles in 6
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(For reference, 1 m is approximately equal to 3 ft
...
The change in speed divided by
the time it takes to make the change is called the acceleration
...
Notice that although in everyday language the word “acceleration” is
used only to refer to a gain in speed, if v0 is larger than v, the acceleration is
negative and is actually a deceleration
...

(a) What part of the equation represents the change in speed? __________
(b) If a car takes 5 seconds to increase its speed from 30 mi/hr to 50 mi/hr, what
is its acceleration? _____________________ 
Answers:   (a) vf – v0;  (b) 4 miles/hour per second (4 mi/hr/s)

4

The unit of acceleration in the problem you just solved is “miles per hour per
second,” or “mi/hr/s
...
”
Suppose a car starts from rest and accelerates at 2 m/s2 for 3 seconds
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 1 second

5

Suppose that, starting from rest, your new truck accelerates at a rate of 5 mi/hr/s
and it continues this acceleration for 8 seconds
...
)
To solve this problem, first rewrite the acceleration equation from frame 3 as:


vf

v0

a t

This is a useful form of the acceleration equation because it says that the
speed of the object after some time (vf) depends on its starting speed (v0), how
quickly its speed is changing (a), and how much time has elapsed (t)
...
In this case, v0 is zero since the truck
started from rest
...
 
Answer:  40 mi/hr (0 + 5 mi/hr/s · 8 s = 40 mi/hr)

4  BASIC PHYSICS

6

MOTION DIAGRAMS
It is helpful to visualize the motion of an object using motion diagrams
...
The photo would look like
figure (1) here:
|------speeding up-----|--------constant speed--------|-------slowing down-------|
(1)

(2)

|

|

a

a=0

|

a

|

We can represent the car’s motion using a motion diagram, as shown in
figure (2)
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At
the beginning, when the car is increasing in speed, the spacing between the dots
increases because the car travels a greater distance in each successive instance
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Finally, when the
car slows down, the spacing between the dots decreases because the car travels
a greater distance in each successive instance
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The longer the arrow,
the greater the speed
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When the car is increasing in speed, its acceleration is in the same direction
as the car is moving
...
When the car is moving at a constant speed, its
acceleration is zero
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(b) For each section of the motion diagram, indicate the direction of the object’s
acceleration
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B: The object is moving left
and speeding up
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(b) A: Acceleration is zero
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C: Acceleration is to
the right
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8
m/s2
...
8 m/s
by the end of the first second and 19
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(a) What is its speed after 3 seconds? _________________________
(b) What is its speed after 5 seconds? ________________________ 
Answers:  (a) 29
...

Since the ball is moving downward and speeding up, the acceleration is also
downward
...
8 m/s
...
8 m/s

2s
9
...
6 m/s

1s
19
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4 m/s

0s
29
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4 m/s, as in figure (2)
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8 m/s for every second that passes
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We see that, in both cases, the acceleration of the
ball is 9
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(a) In figure (2), what would be the speed and direction of the ball after (i) 4 seconds? (ii) 5 seconds? ___________________________
(b) In figure (2), at what time would the ball return to the person who tossed
the ball upward? ______________________________ 
Answers:  (a) (i) 9
...
6 m/s downward;  (b) 6 seconds

9

ACCELERATION EQUATIONS
The equation relating acceleration, the distance traveled, and the time elapsed is:


d

1
a t2
2


v0 t

where v0 is the starting speed, a is the acceleration, and t is the time elapsed
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8 m/s),
it has fallen a distance of 4
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8 m/s2 · 1 s2 = 4
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After 3 seconds of fall, how far has it fallen? _________________________ 
Answer:  44
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8 m/s2 · (3 s)2 = 44
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8 m/s, the ball fell only 4
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This is
because the ball wasn’t moving at a constant speed of 9
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8 m/s
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9 m/1 second = 4
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For an object that is speeding
up or slowing down at a constant rate (i
...
, constant acceleration), the average
speed of the object during a time t can also be determined with the following equation:


v avg

vo

vf
2



which is the simple mathematical average of its starting speed and its speed at
time t
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Motion  7

Take the example in the previous frame
...
1 m
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We know that v0 = 0 (because the object is dropped) and that after 3
seconds, vf = 29
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Using the equation above, the average speed during those
3 seconds is (0 m/s + 29
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7 m/s
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7 m/s in those 3 seconds, the distance traveled in that
time is 14
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1 m
...

A car traveling at 20 m/s accelerates at a rate of 5 m/s2 for 10 seconds
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(d) Check your answer to (c) by using

d

v0 t

1
a t2  
2

Answers:
(a) 70 m/s (20 m/s + 5 m/s2 · 10 s = 70 m/s)
(b) 45 m/s ([20 m/s + 70 m/s]/2 = 45 m/s)
(c) 450 m (45 m/s · 10 s = 450 m)
(d) 450 m (20 m/s · 10 s + ½ · 5 m/s2 · (10 s)2 = 450 m)

11

VELOCITY: A VECTOR QUALITY
Often speed does not tell us all we want to know about a motion
...
You would also need to know in which direction he went
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Identify the two descriptions below
as speed or velocity
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The quantities with arrows are
vectors
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The
symbol d , called the object’s displacement, is defined as the straight-line distance
from the object’s starting position to its final position, including the direction
from start to finish
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2 m east
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All quantities
that are not vectors are called scalars
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(a) velocity _________________________
(b) speed _________________________
(c) time _________________________
(d) displacement _________________________ 
Answers:  (a) vector;  (b) scalar;  (c) scalar;  (d) vector

14

As you might have guessed, acceleration is also a vector, since we must take into
account its direction
...
)
To see the importance of vectors in a simple situation, consider the following example: Suppose a jogger leaves their house and jogs north 300 ft to the
streetlamp on the corner
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We will calculate the jogger’s average velocity
for the 2 minutes
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)

(a) Which of the three distances given in the figure is the displacement d ?
_____________

Motion  9

(b) What is the jogger’s average velocity?
______________________________________
(c) What is the total distance (not displacement)
traveled by the jogger? __________________

400 ft

300 ft
500 ft

(d) What is the average speed (not velocity) during
the 2 minutes? ________________________ 
Answers:  (a) 500 ft;  (b) 250 ft/min in a direction
between north and west;  (c) 700 ft;  (d) 350 ft/min

This example shows that velocity and speed
are definitely different things
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15

A VECTOR APPLICATION: PROJECTILE MOTION
Imagine a moving hot-air balloon that drops a sandbag
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An interesting thing occurs: as the sandbag falls, it continues moving forward at the speed that the balloon had when the sandbag was dropped
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The sandbag
1s
continues forward as if it had not
4
...

The figure assumes that the balloon
3s
is traveling at 12 m/s, and it shows
the sandbag at intervals of 1 second
beginning when it is dropped
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Now note its downward
motion
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8 m/s
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6 m/s;  (c) 12 m/s;  (d) 29
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Although
the actual velocity of the sandbag is neither straight down nor horizontal, we
can consider its motion to be a combination of a downward motion and a horizontal motion
...

We will return to projectile motion later in this chapter and again in the next
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The skateboarder is
rolling along on a flat surface and then jumps straight upwards
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* Just like the previous example with the sandbag and
hot-air balloon, the skateboarder’s vertical motion (rising and falling) is independent of their horizontal motion (moving forward at constant speed)
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1 s

0
...
3 s

0
...
5 s

If the skateboard is rolling forward at 5 m/s and the skateboarder jumps up
with an initial vertical speed of 2
...
1 second, what are the skateboarder’s horizontal and vertical
velocities? _________________________
(b) At the end of 0
...
5 seconds, what are the skateboarder’s horizontal and vertical
velocities? _________________________ 

 Of course, we have to assume the effects of friction slowing the skateboard down are very small
...
47 m/s upward (since the vertical speed changes by 9
...
98 m/s every 1/10th second)
(b) 5 m/s forward and 0
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45 m/s downward

17

ADDING VELOCITIES: ANOTHER VECTOR APPLICATION
Suppose a person is walking on a treadmill at 3 mi/hr
...
The person’s
­forward-walking velocity of 3 mi/hr is canceled by the treadmill belt’s backward
velocity of 3 mi/hr
...

(a) What happens if the person walks forward at 2 mi/hr on the same treadmill?
_________________________ 
Answer:  The person will move backward at 1 mi/hr and eventually fall off the
treadmill
...
Addition of vectors is most easily accomplished by using scale drawings—the “graphical” method of vector addition
...

Part 2 uses arrows to represent the velocities of the boat and the river
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8 m/s and your rowing velocity is 1
...
In part 3, the arrows are shown hooked end-to-end, but they
each keep the same length and are pointed in the same direction as the velocities
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8 m/s (2 cm)

1
...
This vector will represent the resulting velocity of the boat, due to both
your rowing and the river current
...
Go ahead
and draw it now, then measure it
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5 cm

19

Since we used 1 cm to represent 0
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2 m/s (5
...
4), pointing in a direction between the velocity of the river current and your rowing velocity
...
(This is because
your rowing velocity was faster than the river current and thus affects the resultant velocity of the boat more than does the river current
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40 m/s), use the space below
to draw the vector diagram if the rowing velocity is 1
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00 m/s
...
0 m/s (5 cm)
1
...
5 cm)

7
...
0 and 8
...

You should get between 2
...
20 m/s
...
In
part 1 of the figure below, a 3-cm arrow represents this velocity
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Just as was
done previously, one arrow is moved so that its tail falls on the head of the other,
shown in part 3
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_________________________
(b) What is its length? _________________________
(c) How much speed does this represent? _________________________ 
Answers:  (a) It is drawn from the tail of the first to the head of the second;
(b) 2
...
)

21

Let us return once again to projectile motion and the example of the sandbag
being dropped from the hot-air balloon
...
At that time the
forward speed of the sandbag is still 12 m/s
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6 m/s
...
 

14  BASIC PHYSICS
Answer:
12 m/s (4 cm)

Scale: 3 m/s = 1 cm

19
...
5 cm)

This drawing uses a scale of 1 cm to represent 3 m/s
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6 cm long, so the total velocity is 23 m/s
...
Use a separate
sheet of paper for your diagrams or calculations
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1
...
________________________
2
...
How long does it take to
go the distance? ________________________
3
...
Three seconds later its speed is
14 m/s
...
The acceleration of gravity in metric units is___________________
5
...
An object falling from rest reaches a speed of __________ m/s after falling
5 seconds
...
) At this time it has fallen __________ m
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A car moving at 50 m/s slows down at a rate of 5 m/s2 until it comes to rest
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Distinguish between speed and velocity
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Suppose you are a passenger in a car moving at 55 mi/hr
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Just before it hits the seat, how fast is it
traveling forward? What is happening to its downward speed at this time?
________________________
10
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The person’s paddling velocity is 1
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5 m/s north
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Optional
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What is the resultant speed
of the drone? Describe the resulting direction
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1
...
(frame 1)
2
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4 m/s/s, or 4 m/s2 (frames 3–5) 
4
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8 m/s2 (frame 6)
5
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49 m/s; 122
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(a) 10 seconds; (b) 25 m/s; (c) 250 m

16  BASIC PHYSICS
8
...
(frames 11–14)
9
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(frame 15)
10
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5 miles/hour; the direction is east of north, or if you have a protractor you can
measure it to be 37° east of north

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