Kinematics: What is velocity and acceleration?

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14 Νοε 2013 (πριν από 3 χρόνια και 9 μήνες)

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Kinematics:

What is velocity and acceleration?

Let’s Review

v =
d


t

Distance traveled (m)

Time taken (sec)

Average Velocity


(m/sec)

Instantaneous Velocity
: the speed at any given
moment (like what your speedometer shows)

Slope of Position
vs

Time graph is the Average
Velocity


The
slope
of a line is the ratio of the “rise” (vertical
change) to the “run”(horizontal change) of the line.


Constant Speed


On a Velocity
vs

Time graph constant velocity is a
straight line

Area under the velocity vs time graph is equal to the
distance travelled.

What is a Motion Diagram?


Motion Diagram: Is a more sophisticated dot
diagram that conveys more information about the
situation.


What do the arrows indicate?



What does the length of each arrow indicate about the
motion of the object?


Change in Velocity


What must you do to the first velocity arrow to get
the second velocity arrow? What direction? How
much?




The arrow you drew to show the difference between the
velocity arrows is called a
∆v or change in velocity arrow
.



What does the ∆v arrow tell you about the motion of the
object?

Let’s Try!

Lesson 11: Speeding Index

Motion of a
Falling Object


Using the video of the falling object we have collected the
following data:










Draw a motion diagram.


Plot a position time graph.


Does this object represent an object with constant velocity?
Explain how you know.

What is Acceleration?


Acceleration is a
vector quantity

that is defined as the rate
at which an object changes its
velocity


There are 3 types of acceleration:


If an object is increasing in speed (+ acceleration)


If an object is decreasing in speed (
-

acceleration, also called
deceleration)


Or if the object changes direction (+ or
-
)


How do we calculate
Acceleration
?


Acceleration

is the change in speed over the change in time.


The slope of the speed versus time graph is the acceleration.

How to Solve Motion Problems

Rearrange the equation to get final velocity

How do we determine the distance travelled by the object if
velocity is changing?

Equations to Remember

Motion Graphs

0

a

v

t

t

x

t

x

Motion Graphs

0

x

a

v

t

t

t

x

Starting Point

Direction


Velocity

Acceleration

0


+
Positive

+

V
(
speeding up)



+c
onstant

Acceleration Example #1

Δ
v from +5 to +10 m/s requires

a +5 m/s/s acceleration!

V (m/s)

a (m/s/s)


0


+5



+ 5




+ 5


+10


+ 5


15



+ 5

Motion Graphs

0

a

v

t

t

t

x

x

Starting Point


Direction


Velocity


Acceleration

Positive (+)

+V
(
slowing down)



-
c
onstant

0

Acceleration Example #2

V (m/s)

a (m/s/s)

+ 10



-

5


+ 5



-

5


0



-

5

Δ
v from +10 to + 5 m/s requires

a
-

5 m/s/s acceleration!

Motion Graphs

0

x

a

t

t

v

t

x

Starting Point


Direction


Velocity


Acceleration


above


negative (
-
)

-
V (speeding up)

-
constant

Acceleration Example #3

Δ
v from
-
5 to
-
10 m/s requires

a
-
5 m/s/s acceleration!

Direction is negative (
-
), velocity is increasing (+)

Therefore acceleration is (
-
)

V (m/s)

a (m/s/s)


0
-
5


-

5




-

5


-
10




-

5


-
15



-

5

Motion Graphs

0

a

t

x

t

x

v

t

Starting Point


Direction


Velocity


Acceleration


above


negative (
-
)

-

V (slowing down)


+
constant

Acceleration Example #4

V (m/s)

a (m/s/s)

-

10



+ 5


-

5



+ 5


0



+ 5

Δ
v from
-
10 to
-
5 m/s requires

a +5 m/s/s acceleration!

Direction is (
-
), velocity is slowing down (
-
)

Therefore acceleration is (+)

Summary of Velocity
&
Acceleration

V E L O C I T Y


A
C
C
E
L
E
R
A
T
I
O
N

+

-

+

Moving positive
direction; Speeding up

+ acceleration

Moving negative
direction; Slowing down

-

acceleration



-

Moving positive
direction; Slowing down

-

acceleration

Moving negative
direction; Speeding up

+ acceleration

Direction of Motion

Action/Sign of
Velocity

Sign of
Acceleration


















Determining signs for velocity and acceleration

Increasing speed

+
direction

+

Decreasing speed
+
direction

-

-

Increasing speed

-

direction

Decreasing speed

-

direction

+