INTRODUCION

Mechanics is the branch of Physics that deals with the motion of objects and the forces that change it.
Mechanics is divided into 2 areas called kinematics and dynamics . Kinematics describes the motion
of objects without reference to the forces that act on them. Dynamics, on the other hand, is the
study of the explicit relationship between forces and their effect on motion.
Galilei Galilo is the one who introduced this branch of Physics. He did study Free Fall
and motions long incline planes. He described the motion of objets in free-Fall.
(see the bug and the elephant. we neglect the presence of air).


DISPLACEMENT

The displacement vector ds is a vector that points from the initial position to the final position.


We will only deal with motion along a straight line. In such a case, a displacement that points to the West
is assigned a positive value, and a displacement in the opposite direction is assigned a negative value.
A fish swims 500m to the West . ds =
A fish swims 500m to the East. ds =



AVERAGE SPEED

The average speed of an object is defined as the distance traveled divided by the amount required by the amount of time required to cover this distance. Vav = ds / dt  .   ds is the distance.

1/ How far does a jogger run in 1.5 hours (5400s) if his average speed is 2.22 m/s ? in m and in km.


2/ A bicycle has an average speed of 5mi/hr. How far it will travel in 2 hr ? in miles, in kilometer.

3/ convert 70 km per hour to miles per hour

4/ What units would have an approriate size for measuring the average speed with which a blade of grass grows ? m/s ? cm/s ?  km/s ?

5/ A traveler covers a distance of 460 miles in a time of 8 hours. what is the average speed for this trip ?

6/ A traveler covers a distance of 1.8 km in a time of 30 minutes. what is the average speed in km/h ?

7/ A person in a hurry averages 62MPH on a trip covering a distance of 300 miles. What time was required to travel that distance ?

8/ A hiker walks with an average speed of 1.2 m/s . What distance in km does the hiker travel in a time of 1 hour ?



9) Fill the table:

MPH = mi/h	km/h	m/s
20 MPH	?	?
?	64 km/h	?
60MPH
		36 m/s
	160 km/h

10) Look at this map:




What is the average speed between Kingman and Phoenix ?
between Flagstaff and Phoenix  ?










11) Get graph a paper. (you will need graph papers for this class)

The average speed of a car is 40mi/h
Fill the table :

time (hr)	distance (mi)
1	40
2	...
3	...
4	...
5	....
6	....

What is the relationship between the distance and the time ? d = ______
d is called the dependant variable and t the independant variable.
Each time the time increases by 1 the distance increases by  _______  ?

graph  distance versus time.  label the coordinates and don't forget the title. Find a good scale
for each of your axes.

The graph of d =(Vav) t is a ___________________. This equation is a ____________ equation.


What is the slope of the line ? (slope= rise/run = change in y / change in x ).

Conclusion:
the average speed is the ratio of the distance covered (change in y) to the time elapsed (change in x).
The average speed is the __________ of the straight line in a position-time graph.

12) get a graph paper:
The following table records the distance covered by a toy car and the time elapsed.
plots the points and find best fit lines to go through the points. you should find 4 lines.
time = x    and distance = y
 

time (s)	distance (cm)
0	0
5	4.1
10	7.9
15	12.1
20	16.0
25	16.0
30	16.0
35	18.0
40	20.1
45	21.9
50	24.0
55	22.1
60	20.0

graph the relationship   . Describe the 4 parts of the motion. (you should find 4 lines)
Find the average speeds by computing the 4 slopes.

13)  A cyclist maintains a constant velocity of + 5m/s (that is 5 m/s to the right. THe "+" is for the direction).
At time t = 0.0 , the cyclist is 250m from point A.
A. Plot a position-time graph of the cyclist 's location from point A.
B. Whay is the cyclist poition from point A at 60.0 s ?
C. What is the displacement from the starting position at 60.0s ?

14) Both car A and car B leave school when a clock reads zero. Car A  travels at a constant speed
75km/h, and car B travels at a constant speed 85km/h.
A. Draw a position-time graph showing the motion of the car
B. How far are the 2 cars from school when the clock reads 2.0 h ? CAlculate the
distances using the equation of motio and show them on your graph.
C. Both cars passed a gas station 120km from the school. When did each car pass the
gas station ? calculate the times and show them on your graph.

15) Graph and find the slope. The slope is the ______________
time (s)   position (m)
0                 0
1                60
2              120
3               180
4               240
5               300

DISPLACEMENT VERSUS TIME

What is the area of a rectangle ?

What is the relationship between average velocity  and displacement ?

 Displacement  covered by an object moving with an average velocity  Vav during t :  ___________

If you are given the graph instantaneous velocity  versus time (below), could you find the displacement of the car?



Using the graph above, describe the motion of the toy car.
compute the displacement  covered in each part of the motion/ Count 4 parts.


We can find the displacement this way even when  the graph velocity vs time
does not involve are not rectangles. The process is more complicated as
you need you know how to integrate over time to find the area under a
more complex curve.

16)
A) graph :
time (s)      velocity (m/s)
0                      0
1                       20
2                       40
3                       60
4                       80
5                        100

B) WHat is slope of the line ? Can you find the equation of the line ?
What does the slope represent ?

C) Can you find the displacement covered when t = 1 s ? (find the area below the line)
                                                                          t=2s ?
Fill the table :
time (s)      displacement (m)
0
1
2
3
4
5
                                                                          

INSTANTANEOUS SPEED

A speedometer measures the instantaneous speed.  
It tells us how fast we go at a given instant in time. It tells us
little how long it will take to travel several miles. Unlike the average speed.
We can find the instantaneous speed by
computing the average speed over a short time interval in which the speed does not change appreciately.
Vinst = (distance)  / t   with t very very small. . If you take calculus, you will find out that Vinst is the
derivative of the ratio distance / time. Same thing is true for the instantaneous velocity.





Variations in instantaneous speed for a portion of a trip.

VELOCITY

speed is a scalar and velocity is a vector. Velocity has
therefore a magnitude and a direction. speed tells you "how fast".
Velocity tells you "how fast and which direction"
for example: A car can moves at 20m/s , 60 degrees East of North. Can you represent that situation ?

answers

A race cars takes 2 runs. One toward the right. ds= + 604m and dt=2.19s
and one toward the left. ds = - 604m and dt = 2.22s.
Compute the average velocity for each run.
Vav = ds /dt    ds is the displacement.

ACTIVITY
PRINT OUT THE GRAPH and describe the motion. Compute the average speed by computing the slopes.
 page1

LABS

1) How fast do you normaly walk ? using a meter stick or a string, lay out a straight course
for 40 or 50 meters. Use a watch with a second hand or a stop-watch to determine :
- normal speed in m/s
- jogging speed for this same distance.
- sprinting speed for the distance

2) The speed with which hair of fingernails grow provides some interesting measurement challenges.
Using a millimeter rule, estimate the speed of growth of one or more:
fingernails, tornails, hairs. What are the units most appropriate for describing this speed.

3) print out these labs. do only part A and B
materials: motorized toy, inclined plane, stop watch

page1   page2  page3  page4  page5  page 6  page7   page8  page9  page10  

4) another lab
materials: masking tape, 8 stopwatches, soft ball., smooth hallway

page1   page2         page3

Answer these questions:
A. How is average speed computed?
B. What is the difference between average speed and constant speed ?
C. Look at your graph .  Was the ball moving at constant speed along the hall way ? How can you tell ?