Your Basic Kinematics

Motion: speed, velocity and acceleration


Our first example of a “time rate of change,” how quickly slowly something changes in time.

Most of the stuff you see around you is not in motion. Our reference for motion is the surface of the earth and those things at rest relative to it—buildings, bridges, telephone poles, streets, cities, etc.

You’re already familiar with the concept of speed in miles per hour, from reading a speedometer and from seeing speed limit signs. A speedometer registers what’s called instantaneous speed, the speed at one “instant” of time. On your way to work or school, you travel at many different instantaneous speeds, including zero miles per hour when you’re stopped.

Your average speed is the distance you drive to work or school divided by the time it takes to get there. So to find the average speed, you just divide distance traveled by the time of travel,
v = d / t.

Stopping at a stop sign or traffic light is going to increase time, making average speed lower.

EXAMPLE 1: distance = 7.5 miles, time 15 min. Did not have to stop at any stop lights. Want mph, how to get it? 15 min (1 hr/60 min) = 0.25 hr. ` v = 7. 5 mi/ .25 hr. = 30 mph.
EXAMPLE 2: same distance but this time you get stopped at three red lights for 20 sec each. 3 X 20 = 60 sec =1 min. Time to travel 7.5 mi is now . . . 16 min X (1hr/60min) = .27 hr, so we have 7.5 mi / .27 hr = 28 mph.

If you have 15 min to get to work or school, you’ll be upping your average speed by going over 30 after the first stoplight. Then you might actually catch the next one green. Or may have to wait again for less time.

Def. of motion “When an object is undergoing a continuous change in its position we say the object is moving or is in motion.” Change in position relative to what? All those things that are stationary, the totality of which we call a reference frame or rest frame.

“A journey of a thousand miles begins with one step.” The step must be in some direction! When direction must be specified, the quantity becomes a vector. Displacement is the name of the vector representing a distance in some given direction.

Motion can be either constant speed, constant velocity, or accelerated motion. Acceleration itself can be constant or increasing or decreasing but constant acceleration is the only case dealt with in beginning physics classes.

Until Galileo did his experiments with falling and rolling objects, acceleration was not understood and people just thought of “motion.” Galileo did QUANTITATIVE OBSERVATIONS (measurements) that related distance to time (made and used a water clock). Galileo “discovered” acceleration.

Can now calculate average speed, but how do you calculate velocity and acceleration?

First thing to know is they are vectors. In physics, a vector is something that has magnitude and direction. A vector quantity is represented by an arrow. The length of the arrow is the magnitude. The direction is the direction the arrow is pointing.

VELOCITY.
The length of a velocity vector has a special name. SPEED. If you just want to know how fast something is going and don’t care or already know what direction it’s going in, you talk about its speed. Our study of motion starts with speed.

RECALL what came up in first class—the measurements made that day. Speed was one of them. Since you’re most familiar with speed in the context of looking at your speedometer and making sure you’re not going too fast, let’s talk about what a speedometer measures. That’s called instantaneous speed.
Instantaneous speed = speed at one instant of time.

Instantaneous VELOCITY = speed and direction at one instant of time.

If you’re talking on you cell phone (probly shouldn’t be) and you tell someone you’re driving south on Hazel Street at 40 miles an hour, you’re telling them your instantaneous velocity. (Note that this doesn't tell the person where you are on Hazel St.)

Your instantaneous speed or velocity is not by itself going to tell you if you’re going to get to work or class on time. Not unless you start off at one particular speed and don’t stop or speed up all the way there. Your average speed is what determines how fast you get somewhere.

AVERAGE SPEED = distance traveled/ time to travel that distance. ` v = D d/D t. Usually you can just write this as ` v = d/t.
　
　
Also have AVERAGE VELOCITY. First need to have a concept called displacement. Again we have a vector quantity. This time the magnitude of the vector is distance from the starting point, and direction is along a straight line from starting point to ending point.

AVG VELOCITY = displacement/ total travel time. See example in book. Fig. 2.4 Beyond the scope of this class. But should know: if a car returns to its starting point, then the displacement is zero, so the avg. velocity is zero too.

ACCELERATION: ` a = D v/D t = (vf – vi)/ (tf – ti) change in velocity divided by change in time. Usually can write it as just ` a = D v /t, and if vi = 0, can write a =vf/t. vf =at.
　
EXAMPLES ARE GRAVITY, CIRCULAR MOTION, AND PROJECTILE MOTION (object falling due to gravity).

Near the surface of Earth, objects fall with constant acceleration, 9.8 m/s^2.
 How fast will object be traveling when it hits the ground dropped from a certain height? d= ½ gt^2 has time in it. Vf = gt gives v speed in terms of time. We want speed in terms of distance fallen. What to do? Solve one equation for t and substitute into the other equation “eliminate the unknown between the two equations.”
T=vf/g, d= ½ g (vf/g)^2 = ½ vf^2/g. 2dg=vf^2, 

EXAMPLE ONE: How high to hit ground at 60 mph? D = vf^2 / 2g. 60mph (1ft/s / .682 mph) = 88 ft/s. d= 88ft/s ^2 / 2(32 ft/s^2) = 121 ft. Simmons Bank. Wear a seat belt!

EXAMPLE TWO: What is speed if jump from 12 feet? Vf= (2X12ftX32ft/s^2)^ ½ = sqrt(24X32) ft/s = sqrt288 = 17 ft/s (.682mph/1ft/s) = 11.6 mph.

Centripetal acceleration: ac = v^2 / r Example: exercise 17.

Projectile motion: constant velocity in x direction, constant acceleration “g” in y direction. See Fig 2.15.
Figure 2.17 shows 45 degrees as max radius, and shows “complementary angles” of 30 and 60 give same range. “Complementary” means they add to 90 degrees.  This word is different in spelling and meaning from the word "complimentary."  Keep that in mind, or you may wind up complementing someone when you meant to compliment him or her.  Or vice-versa.

Intro lecture

Contents:  measurement, units, significant digits, unit conversions, scientific method.  And a course overview.

Write down your name, what science and math you’ve had, what your future educational plans are.

Assign homework and reading.  Chapt. 1:  4, 8, 10, 16, 18, 20, 24.   Read chapter 2. 

TODAY: measurement; units; scientific method; sig. Digits; unit conversions.

What is a MEASUREMENT? 

A measurement is a quantitative observation.  The observation must be expressed as a number, the number must have some unit.

Tell me about a measurement you made today.  (examples: did you measure a time?  Temp? speed?)  (you didn’t look at your speedometer?)  How can you measure the speed of a car as it passes you when you are on the side of the street?  (prep for next chapter). 

Physical science as detective work, because it’s based on observation and theory, and arguments for or against the theory are based on the observations.  Here is an observation: a car in front of you turned right off 28^th onto Cherry at 12:28 pm.  Let’s say whoever it was turned too fast, without signaling. Depending on how much you know about cars, you might observe what kind of car, color, year.  These are quantitative observations, although color is not very precise (not a number).  Do you like that car, year, color; were you slightly perturbed that the driver turned so fast without signaling?  That’s qualitative—maybe means something in a social science setting, but not physical science.  Qualitative evidence may be used in court if motivation for a crime is being considered, but the physical evidence, if there is any, is most important.

Probably you didn’t use the metric system for any measurement you might have made recently. So right away, physics/physical science is somewhat foreign to you.  Because you come in here and find (will find) that meter sticks measure length and kilograms and grams are used to measure weight.  US is only country not using it.  Committed to it in 1975, but without a timetable or deadline

You need UNITS in order to make a measurement.  You can have a system of units you chose yourself—if you lived as a hermit in the woods, you might have to.  What kinds of things do you need to measure?  LENGTH—to build something, such as a cabin to live in.  TIME—to consistently boil an egg to a desired state.  MASS or weight—seems less important. Can you think of any examples where the hermit would need to know weight?  Again in cooking, may be important.  Or the hermit might want a system to measure his own weight.  Could use pebbles from the creek that are about the same size.  Maybe he weighs 250 pebbles, wants to lose 20 pebbles. 

Possible standard units for the hermit: His walking stick = standard length.  Pebbles of approximately same size=standard of weight (not very accurate).  Dripping water from a coffee can with small hole=time. Very much lacking in precision, but he’s technologically lacking. And what about the hermit’s neighbor, when he tries to tell him how big a fish he caught?  Maybe the neighbor uses different sized pebbles!  Well, he’d hold out his hands, probably, to show how big the fish was, so they’d both understand without reference to standard pebbles or a walking stick unit.        |   

What are the real STANDARDS used in science and industry for length, time, mass?  A STANDARD is a fixed, reproducible value that enables accurate and precise measurements to be taken.  It’s what allows quantitative observations to be made. Metric system or mks system of units is defined in the following way:

LENGTH:   the measurement of space in any direction. The standard of length is the METER, defined as the distance traveled by light in empty space in 1/299,792,485 sec.  The speed of light can be used because it’s a universal constant.

MASS:  the amount of matter an object contains.  Standard of mass is the KILOGRAM, which is the amount of matter in a platinum-iridium cylinder kept at International Bureau of Weights and Measures in Paris.  US has one of these bars also, at NIST headquarters in DC.

TIME: other names for it are duration, period, and interval. The SECOND as a standard is well-defined:  “the duration of 9,192, 631, 770 cycles of the radiation associated with a specified energy-level transition of the cesium-133 atom.”  Einstein and simultaneous events, the last hurdle he jumped in creating relativity.  Time on your own watch as observed by you does not increase or decrease.

DERIVED UNITS & CONVERSION FACTORS:

Derived units are so-named because they’re derived from the fundamental units.  Area and Volume are both derived from length.  These are the ones we’ll use in tonight’s lab.

Another derived unit is speed or velocity, which uses the fundamental units of length and time.  We’ll use it in a later lab, but you measure it all the time, by looking at your speedometer.

You’ll also be using a conversion factor in the lab, converting from meters to feet.

SIGNIFICANT DIGITS:  Will discuss next time, after you have some experience making measurements.

SCIENTIFIC METHODOLGY

Basically, it’s all theory and experiment. Scientific methodology is observation/hypothesis/prediction tested by experiment.    An experiment is a reproducible set of measurements.  A hypothesis becomes a theory if it has been around long enough and passed all imaginable experimental tests many times.  Example:  the atomic theory of matter.  A law is different from a theory.  A law is a concise statement in words or in a math formula about a fundamental relationship of nature. Examples: F=ma.  E=mc^2.  The law of energy conservation.

Scientific attitude is mainly curiosity combined with healthy skepticism, a willingness to accept scientific ideas but not to become too attached to them.   Not about ultimate reality—that is more personal than science, and beyond the realm of science too.

Course overview: Basic physics and chemistry, plus some of their applications in fields such as earth science and astronomy.

Motion is the most basic thing in physics, because without it, there’s no need to worry about space and time.  Motion is even important in why things feel hot or cold—motion of molecules constitutes what we call heat.

Different types of motion result from different forces acting on objects, as described by Newton’s laws of motion and of gravity.  Another way of describing motion is in terms of energy.  Energy offers an explanation of WHY motion can exist, predicting when it will happen, "how much" motion, and what is accomplished by the moving object(s).  However, energy itself is inexplicable except as the “capability of doing work.”  Things get done in this world because work is done, using available energy supplies.

The rest of the course is about how electrons, protons, neutrons, atoms, molecules and light (electromagnetic radiation) all interact as a result of forces, energy and work.  So the big three ideas of this course are FORCE, ENERGY and WORK.  The FEW ideas you can use to describe as briefly as possible what this course was all about.