Kinematics

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

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Topic

Slides

Minutes

1


Displacement

9

27

2


Vectors

13

39

3



13

39

4


Graphs

10

30

5


Energy

10

30

6


Power

5

15

7


Springs

4

12

8


Shadows

3

9

9


Field of Vision

7

21

10


Colors

3

9

11


Concave mirrors

7

21

12


Convex mirrors

4

12

13


Refraction

5

15

14


Lenses

10

30

15


Optical Power

6

18

Kinematics

Click

Kinematics is the study of the motion of objects without regard

to the forces that produce the motion.


There are six important formulas used in kinematics, four are

defined and two are derived (from the defined ones).


Using the following six formulas, all the problems in

kinematics can be solved:

Defined

Derived

s

= distance

v

= velocity

v
i

= initial velocity

v
f

= final velocity

v
a
= average velocity

t = time

a = acceleration

Click

Kinematics
Slide:

Remember

When calculating the average velocity


of an entire trip, use the total time of


the trip, even the time while not moving.

3
.

1

Find the velocity of an

object after falling

freely for 3 m.

Click

3
.

2

Click

t
i
= 2 s to t
f

= 3 s

Use g = 9.8 m/s
2

if you want to be more accurate!

Kinematics
Slide:

3
.

3

A stone is thrown straight up with a velocity of 32 m/s towards

a tree branch that is 25 m high.


With what velocity does the stone hit the branch?

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A)

15 m/s



B)

23 m/s



C)

39 m/s



D)

534 m/s


Kinematics
Slide:

3
.

4

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Kinematics
Slide:

3
.

5

June dropped a stone and measured the time it took to fall

a certain distance. After collecting her data, she plotted the

acceleration versus the time of the falling stone.


Which of the following graphs represents this situation?

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REMEMBER

Falling objects have a constant acceleration.

Kinematics
Slide:

3
.

6

Click

Jack and Jill ride their bikes in an empty parking lot. The graph below

represents the paths of the two cyclists
during a 10 second period.

Which of the following statements is
false
?



A)

At time t = 0, Jill is two meters ahead of Jack.


B)

Jill's speed is always zero.


C)

Between the times t=0 and t=6 s, Jack has a constant speed.


D)

At time t = 8 s, Jack and Jill have the same speed.


E)

At time t = 2 s, Jack and Jill have the same speed.

Note that the slope

represents speed.

Speed = 0

At t = 2 s, Jack’s speed is 1 m/s

but Jill’s speed is 0.

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Kinematics

Slide:

3
.

7

Click

An automobile is traveling at a constant speed along a highway.

Which set of graphs best illustrates the motion of the automobile?

Click

Constant


speed

Zero acceleration

This means

zero

acceleration

Kinematics

Slide:

3
.

8

Sitting on a bench, Stefania sees a cyclist ride by in front of her traveling

at constant speed in a straight line. She observed the trajectory of the

reflector that is fastened to a spoke on the front wheel of the bike.

Reflector

Direction of bicycle

Which of the following represents the
trajectory

that Stefania observes
?

Click

Click

Kinematics
Slide:

3
.

9

Kinematics
Slide:

A ball is thrown vertically into the air with an initial velocity of 20 m/s.

How high does it go?

20 m

3
.

10

A ball travels horizontally with an average velocity of 35 m/s.

How far does it go?

Kinematics
Slide:

35 m

35 m

35 m

35 m

140 m

3
.

11

Click

V

V
H

V
V

V
V

V

V
H

V
V

V
V

V

V
V

V
V

V

V
H

V
V

= 0

V

V
V

V
H

V
V

V

V
H

V
V

V
V

V

V
V

V

Height

Range

The horizontal component of the
velocity

is

constant (
always

the
same
)

The vertical component of the
velocity

is

the
same

as free
fall

The
actual

(or
instantaneous
)
velocity

is

the
vectorial

sum

of the
horizontal and the vertical component
velocities
.

Free fall

Free fall


Projectiles

Projectiles
Slide:

A ball is thrown into the air with a velocity of 40 m/s at an angle

of 30
o
. Determine its: a) Height b) Range

Height

Range

3
.

12

Projectiles
Slide:

A ball is thrown into the air with a velocity of 40 m/s at an angle

of 30
o
. Determine its: a) Height b) Range

3
.

12

Projectiles
Slide:

A ball is thrown into the air with a velocity of 40 m/s at an angle

of 30
o
. Determine its: a) Height b) Range

Height

Range

2 s going up + 2 s coming down

3
.

12

Mike shoots a ball up to his friend Dave who is standing on a

balcony 4.0 m high. Dave misses the ball on its way up but

catches it on its way down as illustrated below.


For how may seconds was the ball in the air
?

Click

NOTE

For simplicity, you may

use 10 m/s
2

instead

of 9.8 m/s
2

for a.

Units are not shown to

keep the formula simple.

Quadratic

equation

3
.

13

If he would have

caught the ball

Projectiles
Slide:

… and good luck!