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Material Type: Notes; Class: Essential Physics; Subject: Physics; University: Duquesne University; Term: Unknown 1989;
Typology: Study notes
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CHAPTER 2 – Motion in ONE Dimension
Definitions:
variable
/symbol
meaning
units
x, y,or r distance m
€
x ,
€
y , or
€
z displacement m
v speed m/s
€
v
velocity m/s
€
a
acceleration m/s
2
t time s
| | magnitude ---
change in
(final-initial)
subscript meaning
o, i initial
f final
An object goes from one point in space to another. After it arrives
at its destination, its displacement is __ than its distance traveled.
Velocity vs. Speed
Both quantities are changes in an object’s position over a certain
period of time. However, one is a vector and one is a scalar. You
must be able to remember which is which because this “small”
difference has enormous consequences.
Which is which?
€
v =
Δ x
Δ t
x
f
− x
i
t
f
− t
i
€
v =
x
Δ t
x
f
x
i
t
f
− t
i
Acceleration
Acceleration is “simply” a change in an object’s velocity over a
period of time.
However, realize the importance of this simple definition…
€
a =
v
Δ t
v
f
v
i
t
f
− t
i
Instantaneous Velocity and Acceleration
€
v =
x
Δ t
x
f
x
i
t
f
− t
i
€
a =
v
Δ t
v
f
v
i
t
f
− t
i
As the interval, ∆, gets smaller and smaller,
€
v =
x
Δ t
d
x
dt
€
a =
v
Δ t
d
v
dt
Since this is an algebra-based course, we won’t be doing any
calculus. What this means for you is that we can “clean up” some
of the notation. We will be dealing only with average speeds and
accelerations. Thus, the formulas you will see on the equation
sheet will look like
€
v =
x
Δ t
x
f
x
i
t
€
a =
v
Δ t
v
f
v
i
t
Acceleration, Deceleration, and Negative Acceleration
What’s the difference? Well…
Acceleration is a change in velocity. Usually people think it means
an object is speeding up. This is not the case because acceleration
is a very general term.
Negative acceleration is more specific, it is something that
depends on your choice of a coordinate system. In this case the
object is experiencing an acceleration in either the
€
x or
€
y
directions (or maybe a bit of both).
Deceleration means an object is slowing down. Conceptually, this
means the velocity and acceleration vectors point in opposite
directions. This is the only way an object will slow down.
Example 3: Chapter 2, #
A tourist, being chased by an angry bear, is running in a straight
line toward his/her car at a speed of 4.35 m/s. The car is a distance
d away. The bear is 30.5 m behind the tourist running at 5.05 m/s.
The tourist reaches the car safely. What is the maximum possible
value for d?
Answer:
Example 4:
A bicyclist makes a trip that consists of two parts, each in the same
direction (due east) along a straight road. During the first part, she
rides for 22 minutes at an average speed of 7.2 m/s. During the
second part, she rides for 36 minutes at an average speed of 5.
m/s. (a) How far has the bicyclist traveled during the entire trip?
(b) What is the average speed of the bicyclist for the trip?
Example 6:
A dog is running in a park and travels 5.00 m due east before
turning and traveling 10.0 m at 30.0˚ south of east. What is the
dog’s displacement?
Answer:
What distance does the dog travel?
Answer:
Example 7:
A car is traveling with a velocity of 10.0 m/s due east. 4.
seconds later the car’s velocity is 5.00 m/s due east. What is the
average acceleration of the car?
Answer:
Kinematics Equations (the “real” ones)
€
r
f
r
i
v
i
t +
at
2
x-component y-component
€
x
f , x
= x
i , x
i , x
t +
a
x
t
2
€
y
f , y
= y
i , y
i , y
t +
a
y
t
2
€
Δ x = v
i , x
t +
a
x
t
2
€
Δ y = v
i , y
t +
a
y
t
2
€
v =
v +
at
x-component y-component
€
v
f , x
= v
i , x
x
t
€
v
f , y
= v
i , y
y
t
From the Meriam-Webster Dictionary:
Kinematics – a science that deals with motion apart from
considerations of mass and force
Equation
Number Equation
€
v
f
= v
i
€
x =
v
i
f
t
€
x
f
= x
i
i
t +
at
2
€
v
f
2
= v
i
2
Apply the solution for quadratic equations to
€
x
f
= x
i
i
t +
at
2
€
AX
2
€
x
f
= x
i
i
t +
at
2
(physics)
Example 8: Chapter 2, #
A motorcycle has a constant acceleration of 2.5 m/s
2
. Both the
velocity and acceleration of the motorcycle point in the same
direction. How much time is required for the motorcycle to change
its speed from (a) 21 to 31 m/s, and (b) 51 to 61 m/s?
