STUDY GUIDE FOR PART I:
VECTORS AND BASIC MOTION
Dr. Johnny B. Holmes
Introduction
Motion in One Dimension
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Introduction
Outline
Supplementary Homework Problems
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In this first part of the course, we consider: 1. what physics is; 2. the
concept of vectors, and 3. the basic description of motion. We first of all
consider what physics is. A first attempt at a definition might be this: Physics is the science that considers the basic
structure of matter, the basic properties of matter, the basic interactions
between pieces of matter, and the basic descriptions of motion. Physics
attempts to describe as many natural phenomena (happenings) as it can in terms
of as few basic principles (laws) as it can.
Note: Natural phenomena are usually very complex things and, to start with, we will be making many idealizations and simplifying assumptions. Once the basic principles are known, you can begin to consider removing some of these simplifying assumptions and try to obtain more and more accurate descriptions of real phenomena.
A. Given the following three equations, solve them for x, y, and z:
ax + by  cz = 5 where a,b,c are the last three digits of your phone number (e.g., 3213448 means a=4, b=4, c=8);
dx + ey + fz = 8 where d,e,f are the last three digits of your (or your parent's) street address or box number
gx  hy  kz = 0 where g,h,k are the last three
digits of your (or your parent's) zip code.
HINT: in the look back stage (step 7), check your answers by substituting in your answers into the equations to show that they indeed work.
B. If the arc length is 3.0 meters and the radius is 12 meters, what is the angle: a) in radians? b) in degrees? c) in revolutions?
C. The moon has a diameter of 3,500_{ }km and is 384,000_{ }km away. a) When viewed from the earth, what angle does the moon make with a person's eye? b) Given that the earth has a diameter of 12,750 km and is 384,000 km away from the moon, when viewed from the moon, what angle does the earth make with an astronaut’s eye?
D. What is the displacement of the point of a wheel initially in contact
with the ground when the wheel rolls forward 3/4 of a revolution? (The radius
of the wheel is 'R' and the 'Xaxis' is the forward direction.) (HINT: break the motion into two part: the translation of the wheel and the rotation of the
wheel. Only look at initial and final points, not the actual trajectory.)
E. A car drives five blocks East, turns North for two blocks, then turns back West for 2 blocks. What is the final position of the car relative to the initial position. Express in both rectangular and polar form.
A. you are on your own  you should be able to check this yourself.
B. a) 0.25 radians, b) 14.32°, c) 0.0398 revolutions.
C. a) 9.11 x 10^{3 }radians
= 0.52°; b) .033 radians = 1.9^{o}.
D. (5.71*R, 1.00*R) or
(5.80*R, 9.9°)
E. (3 blocks East, 2 blocks North) or (3.61 blocks, 33.7° North of East)
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Supplementary Homework Problems
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use with DISCRETE DATA POINTS & NUMERICAL METHODS (computers!)
use with DISCRETE DATA POINTS & NUMERICAL METHODS (computers!)
F. Below are the numerical values of position at specific times. a) Calculate the average velocity between each two times. b) Assuming the average velocities calculated in the previous part are equal to the velocities at the midpoint in the time interval, calculate the average accelerations between the midpoints in time (which are approximately the accelerations at the actual time points.
x (in m) 
T (in sec) 
* 
x (in m) 
t (in sec) 
5.00 
0 
* 
2.50 
4 
4.33 
1 
* 
4.33 
5 
2.50 
2 
* 
5.00 
6 
0.00 
3 
* 
4.33 
7 
G. Below are the numerical values of velocity at specific
times as well as the functional expression for velocity.
a) Using the numerical method calculate the average acceleration during the
time between t=5 seconds and t=6 seconds.
b) To check yourself, use the functional form for a(t)
given below at find the acceleration, a, at t = 5.5 seconds.
c) Using the numerical method calculate the position, x, at t=6 seconds
assuming that x = 3_{ }m when t=0 seconds [i.e., x_{o }= 3 m].
d) To check yourself, use the functional form for x(t)
given below (this was derived using calculus assuming x_{o }= 3 m) to
find the position, x, at t=6 seconds.
HINT: remember for the numerical method you use:
v_{avg} = Dx/Dt,
and a_{avg} = Dv/Dt where Dx = x_{i+1}  x_{i} , Dt = t_{i+1}  t_{i} .
NUMERICAL DATA:
v (0 sec) 
8.0 m/s 
* 
v (4 sec) 
1.6 m/s 
v (1 sec) 
7.4 m/s 
* 
v (5 sec) 
7.0 m/s 
v (2 sec) 
5.6 m/s 
* 
v (6 sec) 
13.6 m/s 
v (3 sec) 
2.6 m/s 
* 


FUNCTIONAL FORMS:
v(t) = 8.0 m/s  (0.6 m/s^{3})t²
a(t) = (1.2 m/s^{3})t
x(t) = 3.0 m + (8.0 m/s)t  (0.2 m/s^{3})t^{3}
H. A car accelerates (assume uniformly) from rest with an acceleration of 1.8_{ }m/s². a) How long a time will it take for the car to reach a speed of 25_{ }m/s ? b) How far will the car have gone in this time? c) How fast will the car be going after 10 seconds? d) How far will the car have gone after 10 seconds?
I. A ball is thrown upwards from the top of a building 14_{ }meters high with an initial speed of 25_{ }m/s. a) How long will it take the ball to reach it's highest point? b) How high will this highest point be? c) How long will it take the ball to hit the ground (at the bottom of the building)? d) How fast will the ball be going when it hits the ground?
J. For the situation in problem G above, graph v(t) versus t. From this graph, be able to qualitatively graph x(t) versus t, and a(t) versus t.
K. Below is a graph of x(t). On the graphs below it, sketch v(t) and a(t).
L. Below is a graph of a_{x}(t). On the graphs below it, sketch x(t) and v_{x}(t) assuming that x_{o }>_{ }0 and v_{xo }<_{ }0.
F.
v (in m/s) 
t (in sec) 
* 
a (in m/s^{2}) 
t (in sec) 
0.67 
0.5 
* 
1.16 
1 
1.83 
1.5 
* 
0.67 
2 
2.50 
2.5 
* 
0.00 
3 
2.50 
3.5 
* 
0.67 
4 
1.83 
4.5 
* 
1.16 
5 
0.67 
5.5 
* 
1.34 
6 
0.67 
6.5 



G. a) a_{num} = 6.60_{
}m/s²; b) a_{cal} = 6.60_{ }m/s²; c) x_{num }=
1.20_{ }m; d) x_{cal }= 1.80_{ }m
H. a) 13.89 sec; b) 173.61
m; c) 18_{ }m/s; d) 90 m.
I. a) 2.55 sec; b) 45.89 m;
c) 5.61 sec; d) 29.99 m/s.