PART 0: SPEED CONVERSION
1) Read.
.  So far, conversions were easy . It was just about solving a proportion problem. (cross-multiply and divide).
Sometimes they are not that easy because they involve ratios. Like convert 30 m/s into km/h  (given 1km= 1000m and 1 h = 3600s).
I am going to teach you a different way to do these kinds of conversions.

First you should remember that 1 is the identity number for multiplication.   so 1 x number = number.
Then also : X/X = 1 and it works also for the units :  km/km = 1    ok?
so here how it goes:
A) V = 30 m /s          you need to get rid of the m  and get a km instead.   You need to use 1000m = 1 km  or  1000m/1km = 1  or  1km/1000m = 1  
If you multiply V   by  1km/1000m  it is like multiplying by 1 and that would be ok. so:
V  = 30 m/s  x  1 km/ 1000m         cross out the m      so V = 0.030 km/s

B) you need to get rid of s and get h  instead at the denominator  using   3600s/1h = 1     (you coud also take 1h/3600s = 1  but we need the s at the top)
V= 0.030 km/s  x   3600s/h  =   10.8 km/h

your turn:
2) 987 m/s = _______ km/hr ;   391 m/s = _______ km/hr ; 921 m/s = ______ km/hr ; 44m/s = ___________km/s

3)Convert 3245 km/h to m/s

4) your turn:
4392 km/h = ________ m/s ; 6321 km/h = _______ m/s ; 6421 km/h = _____ m/s
7000 km/h = _______ m/s

We will see over examples as we go through our chapters. The idea is always the same.

5) A) Because of the expansion of the universe (the space between clusters of galaxies
are stretching) , galaxies or clusters are moving away from us . THis relative speed
increases as the distance increases. (was discovered by Hubble in 1929 who found the
linear relationhsip betwen the speed and the distance of galaxies).
The picture below gives the recessions speeds for some clusters or galaxies..
source: http://astro.wku.edu/astr106/Hubble_intro.html

Convert each speed in mph (miles per hour)

6) The EArth orbit the Sun at a (revolution's) speed of 67000 miles per hour
convert to km/h



7)Find the rotation's speed of Earth in km/h . distance = circumference = 2x pi x R   with R = 6,000km
time = 24 hours.   then convert to miles per hour.

8) the solar system orbits the center of the milky way at a speed of 552km/s
convert to miles per hour.

9) The moon orbits Earth at a speed of 2288 miles per hour. convert to km/h

10) In the air the molecules are moving at speeds greater than 1500km/s. convert to miles per second

11) The sound travels at a speed of 1000ft/s (1000 feet in 1 second).
A) convert in mph.  1 mile is about 5000 ft, 1 hour is 3600 s.
 hint: 1 mile/5000ft = 1    3600s/1hr = 1    1000ft/s = 1000ft/s  x 1 mi/5000ft  x 3600s/hr =
B) In 5 s sound travels ________ miles
hint: 5000ft = 1 mile

12) A)The speed an object (like a space ship) needs to have to leave the Earth is about 7mi/s.
This is called the escape speed. With such a speed, an object can escape EArth gravity.
Convert to km/h

B)Nature loves symmetry. So if an object attracted by the Earth, collapses on it (no initial speed), then
it will hit the Earth with the same speed = ________.

13 ) 1)  The light travels about 10¹³ km in a year of about 10¹³km/year (it is a speed). Using the method described above, find the
speed in m/s.   (hint: 1 year is about pi x 10⁷ seconds  you can check 1 year = 365 x 24 x 60 x 60)

14) the speed of lightning is 60,000 m/s convert to mph


PART I: INTRODUCTION
1) read
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 Galileo is the one who introduced this branch of Physics. He did study Free Fall
and motions along incline planes. He described the motion of objects in free-Fall.
(see the bug and the elephant. we neglect the presence of air).

 

PART II: 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  if his average speed is 2.22 m/s ? in m and in km.
hint: speed = distance / time. First convert 1.5 hours into seconds.

2/ A bicycle has an average speed of 5mi/hr. How far it will travel in 2 hr ? in miles, in kilometer.
(see home page to find the conversion factor)

3/ convert 70 km per hour to miles per hour

4/ What units would have an appropriate 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 ? hint: 60 minutes/1 hr =1

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) light from the sun reaches EArth in 8.3 min. The velocity of light is 3 10⁸ m/s. How far is EArth from the Sun?
hint: convert minutes to seconds

10) you and your friend each drive 50km. You travel at 90km/h ; your friend travels at 95km/h. How long will your friend wait for you at the end of the trip?
hint: you may want to concert to minutes.  Find the time for each person and take the difference.

11) you drive a car for 2h at 40km/h, then for another 2h at 60km/h
A) What is your average velocity ?
hint: Av velocity = total distance/total time
So first, find the distance covered during the first 2h, then the distance covered into the next 2h, find the total distance and divide by the time.

12) A car is moving down a street at 55km/h. A child suddenly runs into the street. If it takes the driver 0.75s to react and apply the brakes, how many meters will the car moved before it begins to slow down.
hint: Find out the distance for a time = 0.75s. Convert 55km/h to m/s first.

13) for muscle to contract, a signal has to be transmitted from the brain to the muscle (hand) back to the brain.
The speed of the signal is about 100m/s. You touch something hot, how long it will take you to let it go ?
(the signal hot needs to go to your brain then back to your fingers. length of arm is about 1 m )



13) You are going to fill the following table.
A) First find the factor to go from mph to km/h.  factor = ______________
(of course you understand that to go from km/h to mph you divide by this same factor. of course, no need to say)

B) Find the factor to go from km/h to m/s . factor = ____________.

(of course, to go from m/s to km/h you divide by this same factor)
C) using these 2 factors fill the table.

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

14) Look at this map:




A) What is the average speed between Kingman and Phoenix ?
between Flagstaff and Phoenix  ?
hint: first find the distance . units MPH
B) trace the displacement vector from Kingman and Phoenix. Using a ruler, find the magnitude of the displacement and its direction/
hint: Find the scale of the picture. measure the distance in cm between Kingman and Flagstaff. that much of cm found is for 120 miles. Then measure the distance between Phoenix and Kingman with a ruler. (follow displacement vector). Convert to miles using the scale. To find This is your magnitude. the direction , use a protractor and find the angle between the displacement vector and the horizontal (a line between Kingman anf Flagstaff). so ds = _____ miles @ _____ degrees south of east.

DISTANCE VS TIME , use your graphing skill. The equation of a linear line is y = m x + b
m is the slope and m is the y-intercept.

PART III: DISTANCE vs TIME, SPEED, USE your graphing skills, MORE PROBLEMS

1) Get graph a paper. 

The average speed of a car is 20mi/h
Fill the table :

x= time (hr)	y= distance (mi)
1	20
2	____________
3	____________
4	______________
5	____________
6	_______________

What is the relationship between the distance and the time ? d = ___ t (or y = ____ x)
Don't use your TI ! the slope is given and the y-intercept = ______ because (0,0) belongs to the line !
This equation is called a ___________ relationship. The distance traveled is _________ to the time elapsed.
d is called the ______________ variable and t the ______________  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. 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.

2) get a graph paper:
The following table records the distance covered by a toy car and the time elapsed.
A) plots the points and find 4 best fit lines to go through the points. you should find 4 parts in your motion
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

B)Describe the 4 parts of the motion.

C) Find the average speeds by computing the 4 slopes. (in cm/s)

3)  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.
 Plot a position-time graph of the cyclist 's location from point A, you can first build a x,y table.
x= time (s) and y = distance from point A (m)

time (s)	position from A (m)
0	250
10	_____
____	_____
----	-------
60	________

B. What  is the cyclist position from point A at 60.0 s ?
C. What is the slope ? its meaning ? What is the y-intercept ? its meaning ?

D. What is the relation between the position and the time ? (that is find the equation of the graph)
y = ____ x + ____ or ds (m) = _____ t (s) + _______


4) 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)  Find the equation of motion for each car.
car A : y = ____x   where y is the distance covered (km) and x is the time(h). or d = ___ t.
car B: y = _____x  or d = _____ t  
If you are still unsure you can fill the (x,y)  value tables  to help you. See below. don't have to if you get it.

CAR A x = time(hr) y = position(km) 0 0 1 _____ 2 _______ 3 ____________ 4 __________ ----- __________

CAR B x = time(hr) y = position(km) 0 0 1 ________ 2 _____________ 3 ____________ 4 __________ --- ____________ ---- __________

B. Use your equations to answer:
How far are the 2 cars from school when the clock reads 2.0 h ? 
car A: d = ____ km
car B: d = _____km

C. Both cars passed a gas station 120km from the school. When did each car pass the
gas station ? Use your equations and solve for the times.


5) Easy. Find the slope. The slope is the ___________. The equation of the graph is _____________
time (s)   position (m)
0                 0
1                60
2              120
3               180
4               240
5               300

6) A steel ball is dropped from a height of 100m above the ground. The distance ground - ball (m)  at various times is recorded in  the TABLE below.

!! this is not a line!!

distance versus time
x= time(s)	y= distance(m)
0	100
1	95
2	80
3	55
4	20

A) Plot a graph paper. draw the curve. What kind of curve is that ?

B) Plot the point in your TI. You need your TI because you are going to find the equation of the parabola. Given the points, the TI will find
the coefficients a,b,c of y = ax² + bx + c
steps to follow to plot the points :
i) turn on plot 1 (2nd Y (for statplot) , ON, ENTER, 2nd MODE ( for quit) )
ii ) Then clear functions in Y. (clear Y1, Y2 ... ). 
 iii)Enter the x-values in L1 and y values in L2 (STAT, EDIT)
iv) to plot: ZOOM  9 (9 is for for ZOOMSTAT)

What kind of graph is that ? not a line. It is a _______________.
Next we are going to find the equation of your scatter plot. (that is your ___________ )

C) The TI is going to find the equation of the parabola. (the best fit parabola). y=ax² +bx + c which is a quadratic equation.
 The TI will find the coefficients a, b, c

To find the coefficients with the TI do:  STAT CAL QUADREG (instead of LINREG) (stands for quadratic regression)
The TI compute the coefficient a, b, c. Write down the coefficients down and write the equation of your graph/
a  = ____, b = _____, c = ______

so y = ____________

let's see how good this equation fits your data. In the TI, enter your equation in Y1= ( Y function)
and then TRACE. Does it fit ?

D)Use the equation found  to find the distance covered
by the ball (that is y) for  t= 2.2s ? t=3.5 s ?   or t= 4.2s ? (plug the times in the equation).

d = _________ m, d = ________m and d= _________m

E) Can you find the x-intercept (the positive one) that will make y = 0 ?  (the equation has 2 solutions, but only makes sense in Physics)
That is the time for which the ball will hit the ground (d=0)? solve the equation y =0
you can solve it using algebra (easy) or you can use the quadratic formula, or you can use SOLVER from TI.
you find for t = _________ s (keep 2 decimals) , y = 0 (the ball reaches the ground)

check if this is correct. plug that number back to see if you get 0.

F) find the second x-intercept. Why this value is not considered in Physics?


AMAZING !
If you still don't get it , here is a video:
HERE IS A MOVIE that shows you how to fit a parabola to a scatter plot and how to find the equation of the parabola
that best fits the data.

7) Members of a physics class stood 25m apart and used stopwatches to measure the time of a car driving down the highway passed each person. The data they compile are shown below:

X = time (s)	Y = position (m)
0	0
1.3	25
2.7	50
3.6	75
5.1	100
5.9	125
7.0	150
8.6	175
10.3	200

Using your graphing calculator to fit a line to a position-time graph of the data and to plot this line.
Find the equation of the best fit line: Y= ________ X

8) Consider an elevator moving down or up at a constant speed.
the relationship between the elevation in meters (d) of the elevator (above gound) and the time t  in seconds is given by the function:
d = 2.5 t
Build a table of values and graph the relationship.  (X-axis = 1 line every 5 seconds )

time (seconds)	elevation (m)
0	---
5	----
10	---
15	---

The mainuplated variable is the ___________, the responding variable is the ____________.
The slope is ___________  (don't forget UNIT!!!).  The slope represents the _________ of the elevator (units ).
Th slope is positive because the velocity is positive because the elevator moves @ ____________

Use the same  graph. At t = 15s the elevator stops for 15 seconds. Complete your graph to show the motion of the elevator. (not moving for 15 seconds).
hint: you can fill the following table to help you

time (seconds)	elevation (m)
15	37.5
20	37.5
25	---
30	--

Then the elevator goes down, at the same speed (2.5m/s) but @  down instead  of @ up.  So the velocity is now - 2.5m/s (instead of +  2.5).
So the relationsip between the elevation d and the time t becomes d = - ____ t.
Fill the table and complete the graph to show the motion of the elevator. (use d = - 2.5 t)

time (seconds)	elevation (m)
30	37.5
35
40
45

9) introduction to graphing quadratic equation. Using your TI. (so get a TI and a graph paper)
more advanced
A) all these equations have something in common:
y = x² , y= x² +5 , y = 3x² +5, y = - 5x² -3x +5, y = (x-3)² +2 ., y= (x-1)²
their graph is a ____________. The "bell" can be upward, downward, narrow or wide, but they are all called ______________.

B) The equation of a parabola has always the form: y = ax² + bx + c.         a, b, c are constants called coefficients.
Find a,b and c for each of the equations given in A).
for example if y = (x+2)²   first you expand the square y = x² + 4x + 4 then you identify the coefficients: a =1, b = 4 and c = 4
another example if y = - 4x²    a = -4, b=0 and c = 0

C) let's see what the graphs of parabolas look like, get a graph paper and trace a (x,y) coordinate system. (include all the quarters)
Use your TI. make sure all your stat plots are turned off. (2nd Y=, 4)
- Enter y1 = x² (Y= , Y1=X²)  graph it  (ZOOM 6). Trace what you see on your graph.
- enter y2 = x² + 3 , graph it. What happened ? (don't erase y1). On the same graph, graph the new parabola.
- enter y2= x² - 5  (erase the previous y2 but keep y1 = x²).  graph it. report the graph on your graph (the same). What happened ?
- These are called rigid transformation. the shape of the parabola does not change. Only the position of the vertex.
try now y2 = 2x².  what happened ? note that the coefficient a is greater than 1/

- try y2 = 0.5x². What happened ? note that a is smaller than 1
- enter y2 = (x-2)² . What happened ? It moves along the __________. but , un expectively to the ____________
- try y2= (x+2)²
- try y2 = (x+2)² +1
- try y2 = - 2x²
- try y2 = x² + 2x + 1

I hope you get a better understanding of graphing quadratic equations.

D) suppose y = 3x² + 2x - 5
you want to find f(2). That is y for x = 2. Using your TI is easy.
enter y1 = 3x² + 2x - 5. Then play with the function table to find the y values. (2nd WINDOW, ASK, GRAPH, TABLE)

E) Now suppose you want to find the x-intercepts of y = 3x² + 2x - 5. that is finding the x for which y =0.
that is solving 3x² + 2x - 5 = 0 . You need to solve for x.  (find the x that will cause 3x² + 2x - 5 to be zero)
Easy there is a magic formula that does that for you. first identify the coefficients.
a = ___, b= ____, c= _____
then the x-intercepts are given by the formula : (srqrt (  ) means take the square root of the expression) )
x1 =( -b + sqrt(b² - 4ac) )/2a
x2 = ((-b - sqrt(b² - 4ac) )/2a
Find the x-intercepts. You are lucky, you get a perfect square. It does not always the case.


PART IV: DISPLACEMENT VS TIME, VELOCITY

1) READ  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"

2) A race cars takes 2 runs. One toward the right. ds= + 604m and dt=2.19s
and one toward the left. ds = - 604m (that is @left) and dt = 2.22s.
Compute the average velocity for each run.  average velocity = total displacement / time
and total displacement = add the vectors displacements . That is total displacement = change in position.
(remember the old captain treasure map ?)


3)

A) This graph shows the displacement (can be negative) of a car vs time.

(there is a typo. the title should be displacement vs time. The displacement is a vector = change in position
= distance with direction)
Describe the 3 parts of the motion. For each part, find the velocity of the car (can be negative, the the car is going @ left
or @ west). Follow the steps:
PART1    0< time <2s (I help you for this part)
The car is moving __________________________ ( not moving ? moving@ left ? moving @ right ? at  a constant speed ? accelerating? )
Every second , the car covers a displacement of _______ m (negative is for @left)
The slope is ______ m/s (the slope is negative. slope = rise/run or easier :  for a run = 1 what is the rise  , how many miles per second?)
The velocity V = ________ @ _______ (magnitude = slope, direction is given by the sign)
PART2: 2< time <4s
The car is ____________________
The line is horizontal, the slope = _____ m/s
The velocity = ____________
PART3: 4 < time <6s
The car is ____________________  @ _________
Every second, the car covers _________ m
The slope is __________
the velocity is ____ @ _____________
B)
build a graph velocity (m/s)  versus time (s)
using the answers you got in A). Note that the velocity
can be negative. (You will get a graph with steps. It is called a piecewise function ).
I will help you in class, when we go over but try anyway.

4) A) From the position-time graph (that is displacement vs time) below
describe the motion of a track runner.



between 0<t<40s      the velocity is V = ____m/s @ ________

between  40<t<70s _________________________

between  70<t<90s  V = ______m/s  @ _______

between 90<t<100s the velocity is V = ______m/s  @ _______ or - _______m/s

B) build a graph velocity (m/s)  versus time (s)
using the answers you got in A). Note that the velocity
can be negative. (You will get a graph with steps or piecewise function).


5) Sketch position-versus-time graph.  just sketch it since I don't give you any number. You don't need to include any numbers.
Just sketch the graph of the motion of:
A) A student walks to the bus stop , waits for the bus, then rides to campus. Assume that all the motion is a long a straight line
hint: there are 3 parts in the motion

B) As student walks slowly to the bus stop, realizes he forgot his Physics lab that is due, and quickly back  home to get it.
hint: 2 parts in the motion. Since he walks back, the position decreases (he get closer to 0 = home) . And he gets closer and a higher rate. (slope negative = downhill but larger magnitude)

6) the position versus time graph below shows the position of an object moving in a straight line for 12s.



A) What is the position of the object at 2s, 6s, and 10s after the start of the motion?
At 2s: ____________

At 6s: ___________

At 10s: ____________

B) What is the object's velocity during the first 4s of motion?

C) What is the object's velocity during the interval from 4s to 6s ?

D) What is the object's velocity during the four seconds from 6s to 10s ?

E) What is the object's velocity during the final 2 seconds from t10s and t  12s ?

F) Draw a motion diagram below to represent the entire 12s of motion.
That is draw a graph velocity versus time. !! units on your graph.
Note that the velocity can be negative.
the graph is made of steps. 

7) A) Describe the motion if this moving car for each time intervals.
Not that the time is in minutes and the position in miles.
Include the velocity with the right sign. (negative = moves backward and positive = moves forward).

B) build a graph velocity(mi/min) versus time (min)
using the answers you got in A). Note that the velocity
can be negative. (You will get a graph with steps )

8) really easy
An object is at rest at the position x = 1m. Draw the graph position(m) vs time(s)
and the graph velocity (m/s)vs time (s)

9)

Describe the motion for each interval. (for the entire 8 hours trip) I do the first interval so you know what to do.
A) during 2 hours 0< t< 2h
the car is moving to the right because the velocity is positive. (@ East)
The speed is constant and equal to 15m/s
B) for 2<t<5
______________________

C) for 5<t<7 h
_________________________________

D) for 7<t< 8 h
______________________________

10) same as 9). Describe the motion of the car.



11) For this problem, remember:
the slope of a line = indicates the steepness of the line.
steeper line means larger slope. gentle line  means smaller slope.
In a graph position vs time, the slope = speed. so larger slope = larger speed.

Observe the graph and answer the questions:
A) during which interval of times, is the object moving the slowest ?

B) Is the object moving the slowest ? (non including the at rest state)

C) IS the object at rest?

D) Does the object has a constant non zero velocity ?

E) Is the object moving to the left?


PART V: VELOCITY VERSUS TIME, HOW TO FIND THE DISPLACEMENT, ACCELERATION

1) A) What is the area of a rectangle ?

B)How can you find the displacement ds (a vector) if you are given the velocity V and the time elapsed t ?
displacement = _____________ x _______________ or  ds = __ ____
Keep this in mind.

C) observe the graph velocity versus time. The velocity is given by a speedometer.
It is called the instantaneous velocity  (we will see that lateR. It is the velocity at a given time).  



between the time 0 < t < 20s, the velocity is about V = _________ m/s.
The time elapsed is t = ________s.
The displacement of the car = ____________m.
hint: ds = V t
The area of the rectangle below the graph, between 0 and 20 s = _____________
So displacement = area under the velocity vs time graph !    write that on an index card.

This will be true even if the area is not a rectangle !

D) Find the displacement for the 3 other time intervals. Remember, displacement can be negative.(in which case, the car is moving @ left )
To find the displacement use the new rule you found in C)

For 20s<t<30s      ds = __________m
For 30s< t < 50s     ds = __________m
For 50s<t<60s          ds = __________m


We can find the displacement this way even when  the graph velocity vs time
does not involve any 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.  (in calculus ). Your instructor will explain the idea to you.

2)

A) graph : (don't use the TI, you don't need it)

x=time (s)      y= velocity (m/s)
0                      0
1                       20
2                       40
3                       60
4                       80
5                      100

B) WHat is slope of the line ? a = ____ m/s/s
You don't need the TI, you see that each time you increase x by 1 (time) , y (velocity) increases by _______ m/s
so the slope is ______ m/s/s. Watch the units !!

C) 
That means  every second 1s , the car increases its speed by ______ m/s
What physical quantity the slope represent ? _____________________
the acceleration is positive because __________________.

D) Can you find the equation of the line ? y = ____ x or velocity (m/s) = _____ x   time (s)   or V = ____t

CONCLUSION: THE ACCELERATION is the CHANGE OF VELOCITY OVER THE CHANGE IN TIME
or ACCELERATION IS THE SLOPE OF THE GRAPH  VELOCITY vs TIME
get an index card to write that down.

E) Can you find the displacement covered after 1 s ? after 2s ? after 3s ? after 4s ? after 5s ? Fill the table.
See hints.   REMEMBER are area triangle = base x height / 2                                     
Fill the table :
time (s) elapsed       displacement (m) covered
0                            __0____________
1  (after 1s)             ______________   (find the area below the graph, base = 1, height = 20 it is a triangle)
2   (after 2s)            ______________  (area of a triangle base =2, height = 40)
3    (after 3s)          ______________    (area of a triangle base =3, height = 60)
4          --                  ______________  --
5           --                 ______________  --
                                                                          

3) Observe graph below represent velocity vs time.
A) Find the displacement for the entire motion. (in miles)
remember area of triangle = 0.5 x base x height.
area of rectangle = width x length


B) find the acceleration for:

0<t<4
a= _________ m/s/s    (acceleration = slope of velocity vs time, you should know that)

4<t<8
a= __________ m/s/s
(hint: find the slope. acceleration = change in velocity / change in time = rate of change of velocity


D) graph acceleration vs time ( you have 2 parts, t<4 and 4 <t <8 )
(it is a piecewise function)

4) Observe the graph below: velocity vs time
A) Find the displacement for the entire motion. (in miles). REmember area of a triangle = 0.5 (base) (height)
area of rectangle = width x length



B) find the acceleration for:
0< t< 2
a = ________ m/s/s

2<t<4
a= ___________ m/s/s

4<t<6
a= __________ m/s/s

6<t<7
a = ____________ m/s/s

7<t<8
a = ___________ m/s/s
(hint: find the slope. acceleration = change in velocity / change in time = rate of change of velocity)

C) graph acceleration vs time ( you have 5 parts)


5) The velocity of  an automobile changes over an 8.0 s time period as shown
in the following table:

x= time (s)	y = velocity (m/s)	x= time (s)	y= velocity (m/s)
0.0	0	5	20
1	4	6	20
2	8	7	20
3	12	8	20
4	16

A) plot the velocity vs time graph of the motion. Use a graph paper please. No TI.

B) Determine the displacement of the car during the first 2.0 s ?
hint: Find the area of the triangle with base = 2s  and height = 8m/s

C) What displacement does the car have during the 4.0 s?
hint: Find the area under the graph for 0 < t< 4s base is 4s

D) What displacement does the car have during the entire 8.0 s?
displacement = area of the triangle + area of a rectangle.


E) Find the slope of the line between t= 0s and t = 4s. WHat does this slope represent ?  a = _______ m/s/s
(hint : the units will help you)

F) Find the slope of the line between t=5.0s and t = 7.0s . What does this slope indicate ?


PART VII:  INSTANTANEOUS VELOCITY + REVIEW

1) A speedometer measures the instantaneous velocity.  
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 velocity.
We can find the instantaneous velocity  by computing the average velocity over a short time interval in which the velocity 
does not change appreciably.
Vinst = (displacement)  / t   with t very very small. . If you take calculus, you will find out that Vinst is the
limit of the average speed when the time becomes very small.





1) Variations in instantaneous speed for a portion of a trip.  Describe the trip.

2) REVIEW
A) DEfine speed

B) The SI units for speed are  ______________.
C) How is instantaneous speed different from average speed ?

D) The equation used for calculating average speed is ___________

E) FAlse or true?
You can determine how fast you were going at the midpoint of a trip by calculating average speed for the entire trip.

3) REVIEW  A student walks 1.5 km 25 minutes, and then, realizing he was late, ran the remaining 0.5 km in 5 minutes. Calculate his average speed on the way to school.

4) What type of speed does an automobile's speedometer display?

5) REVIEW
The slope of a line on a distance-graph represents _____________

6)

A) Draw a point on the graph that represents 200m traveled in 4 seconds. Draw a line connecting this point with the origin (0,). Label this as line A.

B) Draw a point that represents 100m traveled in 10 seconds. Draw a line connecting this point with the origin (0,0). Label this as line B.

C) Calculate the average speed (slope) of lines A and B. Be sure to include units.

7) How speed and velocity differ?

8) Circle the letter of each sentence that describes a change in velocity ( that is change in direction or magnitude).
A) A moving object gains speed
B) A moving object changes direction
C) A moving object moves in straight line at a constance speed
D) A moving object slows down

9) Is the following true or false ? If a car travels around a gentle curve o a highway at 60km/h, the velocity does not change ?

10) A river flows at a velocity of 3km/h relative to the riverbank. A boat moves upstream at a velocity of 15km/h relative to the river. What is the velocity of the boat relative of the riverbank ?

11) Circle the letters of the sentences that are true of instantaneous speed.
A) Instantaneous speed is the total distance covered divided by the time
B) Instantaneous speed is the speed at any instant.
C) The speedometer on a car shows the instantaneous speed.
D) If you traveled 30 kilometers in 1 hour, your instantaneous speed would be 30 km / h/