Motion In A Straight Line
Motion in one direction or motion in 1-dimension is the motion in a straight line. This type of motion is also known as Rectilinear motion. When the object has no kinetic energy and no external force is applied on the object, it remains at rest. When some external force is applied to the object and the object gains motion, it starts to move, if the motion occurs in one direction, it is known as rectilinear motion.
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Uniform Motion
When the object travels with the same velocity throughout its motion, the motion is uniform. The initial and final speeds are the same in this case and the speed is given as,
Speed = Distance/Time
Non-Uniform Motion
When the object does not have the same velocity throughout its motion, it may increase its velocity or decrease it, such type of motion is known as Non-uniform motion. If the velocity keeps on decreasing, the object is decelerating, and if the velocity keeps on increasing, the object is accelerating. The formulae for non-uniform motion are given by Newtons equation of motion.
First equation of motion v = u + at
Second Equation of motion S = ut + 1/2
You Will Get A More Accurate Measure Of Reaction Time If You Do This Several Times And Take An Average Of Your Results
Do a few practice runs before starting to keep records. Be sure that your helper releases the ruler cleanly and at a time that is not predictable. You will get best results if you concentrate on seeing the ruler start to fall. If you let your mind wander, you will get an unusually high value of reaction time. Do not try to anticipate the drop of the ruler. If you do, you will get unusually low values.
Do not discard a value just because it is unusually high or low. If there is a reason to discard it, such as release anticipation, ruler sticking to fingers, or ruler not being cleanly caught, that trial can be discarded. However to discard data just because you do not like the results is contrary to good practice. If you have data points which you suspect are bad, the correct procedure is to take so many other data points that the unusual ones do not affect the final average.
Extensions
If you want to do more experiments similar to this one, there are lots of variations that you can try.
Does the size of the ruler have an effect? Borrow a meter stick and repeat the experiments.
Do you get the same result in the morning when you are fresh as in the evening when you are tired?
You studied your eye-hand reaction time. Can you devise an experiment to test you ear-hand reaction time?
Try having your partner yell bang as the start button of your stop watch is pushed, then you push the stop button as soon as possible.
Astronomers’ Interest In Rt
The term reaction time was coined in 1873 by an Austrian physiologist, Sigmund Exner . He is also credited with discovering the importance of preparatory set in the measurement of RT. Lengthening the preparatory interval increases the trial-totrial variability of the subject’s RTs, thereby increasing the measurement error of the mean RT measured in a given number of trials. Since Exner’s discovery, the use of a specified or optimal preparatory interval became standard procedure in RT measurement.
Arthur R. Jensen, in, 2006
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The Slope Of Rtm Across Increasing Levels Of Rs Complexity
RT is often measured at two or more levels of complexity of the RS in the presented task. The simple difference between SRT and two-choice RT can be regarded as a slope measure because the straight line connecting their means slopes upward . In CRT paradigms with more than two choices or levels of complexity such as the Hick and Sternberg paradigms, in which there is a linear relationship between a subject’s RTm and the various levels of the RS , it is of theoretical interest to measure the slope of the linear relationship. Theoretically, the slope is considered to be a measure of the rate of information processing.
Slope is measured as the regression coefficient, b, in the equation for the linear regression of an individual’s RTm on a measure of variation in RS complexity, such as number of digits in the Sternberg paradigm or the number of bits in the Hick paradigm.2
The Unit Of Measurement Of Time: The Second
In the International System of Units , the unit of time is the second . It is a SI base unit, and has been defined since 1967 as “the duration of 9,192,631,770 of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom”. This definition is based on the operation of a caesium atomic clock.These clocks became practical for use as primary reference standards after about 1955, and have been in use ever since.
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Deriving Formula For Reaction Time
Imagine the case of a free-falling object and the time to react and catch it in order to find the reaction time. Keeping in mind that the initial velocity will be zero since the object is freely falling. Applying the second equation of motion in order to find the Reaction time of the vehicle,
S = ut + 1/2
t2 = 0.204S
Technology For Timekeeping Standards
The primary time standard in the U.S. is currently NIST-F1, a laser-cooled Cs fountain, the latest in a series of time and frequency standards, from the ammonia-based atomic clock to the caesium-based NBS-1 to NIST-7 . The respective clock uncertainty declined from 10,000 nanoseconds per day to 0.5 nanoseconds per day in 5 decades. In 2001 the clock uncertainty for NIST-F1 was 0.1 nanoseconds/day. Development of increasingly accurate frequency standards is underway.
In this time and frequency standard, a population of caesium atoms is laser-cooled to temperatures of one microkelvin. The atoms collect in a ball shaped by six lasers, two for each spatial dimension, vertical , horizontal , and back/forth. The vertical lasers push the caesium ball through a microwave cavity. As the ball is cooled, the caesium population cools to its ground state and emits light at its natural frequency, stated in the definition of second above. Eleven physical effects are accounted for in the emissions from the caesium population, which are then controlled for in the NIST-F1 clock. These results are reported to BIPM.
Additionally, a reference hydrogen maser is also reported to BIPM as a frequency standard for TAI .
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Speedy Science: How Fast Can You React
A swift science activity from Scientific American
GravityIntroductionThink fast! Have you ever noticed that when someone unexpectedly tosses a softball at you, you need a little time before you can move to catch it ? That’s because when your eyes see an incoming signal such as a softball, your brain needs to first process what’s happeningand then you can take action. In this activity, you can measure just how long it takes for you to react, and compare reaction times with your friends and family.BackgroundYou may not realize it, but when your senses pick up clues from the outside worldthe smell of baking cookies, the color of a stoplight, the rrrring! of an alarm clockit takes a fraction of a second for you to recognize that signal and respond. During that time your brain receives information from your senses, identifies a possible source, and allows you to take action. The jam-packed fraction of a second is called your reaction time.This activity teaches you about your brain’s reaction time, but it also relies on the laws of physics. Specifically, you can calculate your reaction time using our handy chart, which is based on how quickly a ruler falls. How do we know how quickly your ruler will fall? Gravity pulls all objects toward Earth’s center at the same speed. If you want to try this out at home, try dropping a tennis ball and a basketball from the same height: They should both hit the ground at the same time!Materials
600 ms. |
Galileo: The Flow Of Time
In 1583, Galileo Galilei discovered that a pendulum’s harmonic motion has a constant period, which he learned by timing the motion of a swaying lamp in harmonic motion at mass at the cathedral of Pisa, with his pulse.
In his Two New Sciences , Galileo used a water clock to measure the time taken for a bronze ball to roll a known distance down an inclined plane this clock was
- “a large vessel of water placed in an elevated position to the bottom of this vessel was soldered a pipe of small diameter giving a thin jet of water, which we collected in a small glass during the time of each descent, whether for the whole length of the channel or for a part of its length the water thus collected was weighed, after each descent, on a very accurate balance the differences and ratios of these weights gave us the differences and ratios of the times, and this with such accuracy that although the operation was repeated many, many times, there was no appreciable discrepancy in the results.”
Galileo’s experimental setup to measure the literal flow of time, in order to describe the motion of a ball, preceded Isaac Newton‘s statement in his Principia:
The Galilean transformations assume that time is the same for all reference frames.
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Calculating Stopping Distance And Reaction Time
When an object gains kinetic energy and changes position, it is known to be in motion. There are three types of motion possible, one dimensional, two-dimensional, and three-dimensional motion. One dimensional motion is the object moving in a straight line, two-dimensional motion is when an object moves covering two axes , three-dimensional motion is when an object moves in all three x-y-z directions. The motion of a body is observed w.r.t a frame of reference, on a graph, the origin is denoted as the frame of reference. Lets learn about the Motion in a straight line in more detail,
Some Typical Stopping Distances
Travelling at 20 mph :
- thinking distance = 6 m
- total stopping distance = 12 m
Travelling at 40 mph :
- thinking distance = 12 m
- total stopping distance = 36 m
Travelling at 70 mph :
- thinking distance = 21 m
- braking distance = 75 m
- total stopping distance = 96 m
It is important to note that the thinking distance is proportional to the starting speed. This is because the reaction time is taken as a constant, and speed = distance × time. However, the braking distance increases four times each time the starting speed doubles.
For example, if a car doubles its speed from 30 mph to 60 mph, the thinking distance will double from 9 m to 18 m and the braking distance will increase by a factor of four from 14 m to 56 m.
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Centripetal And Centrifugal Force
Another common mistake is to state that “the centrifugal force that an object experiences is the reaction to the centripetal force on that object.”
If an object were simultaneously subject to both a centripetal force and an equal and opposite centrifugal force, the resultant force would vanish and the object could not experience a circular motion. The centrifugal force is sometimes called a fictitious force or pseudo force, to underscore the fact that such a force only appears when calculations or measurements are conducted in non-inertial reference frames.
A Variety Of Single And Dual Task Paradigms
RT tasks that make greater processing demands generally have longer RTs and larger correlations with IQ tests and particularly with g, the latent factor common to all such tests. For example, some tasks, like the Hick paradigm, require no retrieval of information, whereas paradigms like the Sternberg memory-scanning task call for the retrieval of information from STM, and the Posner Name Identity-Physical Identity task calls for retrieval of information from long-term memory . The retrieval process takes time. One way to experimentally manipulate the cognitive demands on RT tasks is by requiring the subject to perform two tasks within a brief time period. For example, incoming information has to be momentarily held in STM while performing a second and different processing task after which the information in STM has to be retrieved. This is called a dual task paradigm . Studies that included a battery of both single and dual task RT paradigms are described in Chapter 6 . Besides the Hick task, the other seven tasks consist of the Sternberg and Posner paradigms, which are presented both as single tasks and, in certain combinations, as dual tasks.
Thérèse Botez-Marquard, Mihai I. Botez, in, 1997
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Reaction Time Science Project
For Olympic runners and swimmers, a fraction of a second is often the difference between winning a gold medal or a bronze!
Indeed, its the distance between winning any medal or returning home with nothing but hopes at another chance in four more years.
And while its impact is most dramatic in running events, speed isnt only a matter of crossing the finish line first.
In sports, reaction time, the interval between stimulation and reaction, often determines who wins and who loses. Even more importantly, in real-life situations, like when driving a car, it can mean the difference between life and death.
Measure your reaction time with the following project.
What You Need:
What You Do:
1. Have your partner sit or stand with their arm on the flat surface so their wrist extends beyond the edge.
2. Hold the meter stick vertically above your partners hand, with the 0 end of the stick just above their thumb and forefinger, but not touching them.
3. Instruct your partner to catch it as quickly as possible as soon as they see it begin to fall.
4. Without warning your partner, drop the meter stick.
5. Record how far it fell before your partner caught it. Consult the reaction time table to determine reaction time. Repeat at least two more times.
6. Switch places with your partner and repeat.
What Happened:
For further study:
Electromagnetism And The Speed Of Light
In 1864, James Clerk Maxwell presented a combined theory of electricity and magnetism. He combined all the laws then known relating to those two phenomenon into four equations. These vector calculus equations which use the del operator are known as Maxwell’s equations for electromagnetism.
In free space , the equations take the form :
Prerequisites |
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- is the speed of light in free space, 299 792 458 m/s
- E is the electric field
- B is the magnetic field.
These equations allow for solutions in the form of electromagnetic waves. The wave is formed by an electric field and a magnetic field oscillating together, perpendicular to each other and to the direction of propagation. These waves always propagate at the speed of light c, regardless of the velocity of the electric charge that generated them.
The fact that light is predicted to always travel at speed c would be incompatible with Galilean relativity if Maxwell’s equations were assumed to hold in any inertial frame , because the Galilean transformations predict the speed to decrease in the reference frame of an observer traveling parallel to the light.
It was expected that there was one absolute reference frame, that of the luminiferous aether, in which Maxwell’s equations held unmodified in the known form.
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Youll Then Calculate The Time It Fell With This Equation
References1. Hewitt, P.G. Conceptual Physics, 7th Ed., pp 29-32.
2. Crummet, W. P. and Western, A. B., University Physics , advance copy, pp 52-59.
3. Ostdick, V. S. and Bord, D. J., Inquiry Into Physics, 2nd Ed., pp 28, 34-37.
4. Serway, R., Principles of Physics, pp 41-49.
5. Tipler, P.A., Physics, pp 33-36.
6. Young, H.D., Physics, 8th Ed., pp 39, 44.
Time In Quantum Mechanics
There is a time parameter in the equations of quantum mechanics. The Schrödinger equation is
Prerequisites |
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The more precisely one measures the duration of a sequence of events, the less precisely one can measure the energy associated with that sequence, and vice versa. This equation is different from the standard uncertainty principle, because time is not an operator in quantum mechanics.
Corresponding commutator relations also hold for momentum p and position q, which are conjugate variables of each other, along with a corresponding uncertainty principle in momentum and position, similar to the energy and time relation above.
Quantum mechanics explains the properties of the periodic table of the elements. Starting with Otto Stern‘s and Walter Gerlach‘s experiment with molecular beams in a magnetic field, Isidor Rabi , was able to modulate the magnetic resonance of the beam. In 1945 Rabi then suggested that this technique be the basis of a clock using the resonant frequency of an atomic beam.
See dynamical systems and chaos theory, dissipative structures
One could say that time is a parameterization of a dynamical system that allows the geometry of the system to be manifested and operated on. It has been asserted that time is an implicit consequence of chaos : the characteristic time, or rate of information entropy production, of a system. Mandelbrot introduces intrinsic time in his book Multifractals and 1/f noise.
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