[fence]
discussion
speed
What is the difference between two identical objects moving at different speeds? Most everyone knows that the fastest mover (the one with the greatest speed) goes further in the same amount of time as the slowest mover. Either that or they will tell you that the fastest mover will get there faster than the slowest one. Whatever the speed, it involves both distance and time. "Faster" means "farther" (greater distance) or "earlier" (less time).
Doubling your speed would mean doubling the distance covered in a given time. Doubling the speed would also mean halving the time it takes to travel a given distance. If you know a little math, these statements make sense and are useful. (The symbolvis used for speed because of the speed to speed relationship, which will be discussed shortly).
 Speed is directly proportional to distance if time is constant:v∝s(tpermanently)
 Speed is inversely proportional to time when distance is constant:v∝^{1}_{t}(spermanently)
The combination of these two rules gives the definition of velocity in symbolic form.
v=  s 
t 
☞ This is not the final definition.
Don't like symbols? Well, here's another way to define speed.speedis the rate of change ofdistancewith time.
To calculate the speed of an object, we need to know how far it has traveled and how long it took to get there. "Further" and "before" correspond to "faster". Let's say you drove from New York to Boston. The distance by road is approximately 300 km (200 miles). If the trip takes four hours, what was his speed? Applying the above formula we get...
v=  s  ≈  300km  = 75 km/h 
t  4 hours 
That is the answer that the equation gives us, but how correct is it? it was 75 km/hthecar speed? Yes, of course it was... Well, maybe, I think... No, it can't betheSpeed. Unless you live in a world where cars have exceptional cruise control and traffic flows ideally, your speed must surely have varied during this hypothetical journey. So the number calculated above is notthespeed of the car is theAverage speedfor the whole trip. To emphasize this point, the equation is sometimes modified as follows...
v=  ∆s 
∆t 
The bar above itvindicates an average or mean and the∆The symbol (Delta) indicates a change. Read it as "Vbar is deltaess over deltatee". This is the amount we calculate for our hypothetical trip.
In contrast, a car speedometer shows this.instantaneous speed, that is, the speed determined in a very small period of time: an instant. Ideally this interval should be as close to zero as possible, but in reality we are limited by the sensitivity of our meters. In the mind, however, one can imagine calculating the average speed over smaller and smaller time intervals until we have actually calculated the instantaneous speed. This idea is written symbolically as...
v= 
 ∆s  =  SD  
∆t  dt 
or, in the language of calculusspeedis the first derivative ofdistancein relation to time.
If you're new to calculus, don't worry too much about this definition. There are other, simpler ways to find the instantaneous speed of a moving object. On a displacementtime diagram, velocity is equal to slope, and therefore the instantaneous velocity of an object with nonconstant velocity can be found from the slope of a line tangent to its curve. we take care of thislaterin this book.
speed
To calculate the speed of an object, we need to know how far it has traveled and how long it took to get there. A wise man would then ask...
What do you mean withhow far? Do you want thedistanceor thechange?
once upon a time there was a wise man
Your answer to this question determines what you calculate: speed or speed.
 Average speedis the rate of change ofdistancewith time.
 Average speedis the rate of change ofchangewith time.
And for the calculation people out there...
 instantaneous speedis the first derivative ofdistancein relation to time.
 current speedis the first derivative ofchangein relation to time.
Velocity and speed are related in a similar way to distance and displacement. Velocity is a scalar and velocity is a vector. The velocity gets the symbolv(italics) and Velocity gets the symbolv(bold font). Average values get a bar above the symbol.
Average speed 
 
instantly speed 

Average speed 
 
instantly speed 

Displacement is measured along the shortest path between two points, and its magnitude is always less than or equal to the distance. The magnitude of the change approaches the distance as the distance approaches zero. That is, the distance and the offset are effectively equal (the same size) when the interval examined is "small". Since velocity is based on distance and velocity is based on displacement, these two quantities are effectively equal (have the same magnitude) when the time interval is "small" or, in computational language, the magnitude of velocity average velocity of an object approaches its average speed. as the time interval approaches zero.
∆t→0  ⇒  v→v 
The instantaneous velocity of an object is then the magnitude of its instantaneous velocity.
v=v
Speed tells you how fast. Velocity tells you how fast and in which direction.
units
Velocity and speed are measured with the same units. The SI unit for distance and path is the meter. The SI unit of time is the second. The SI unit of velocity and velocity is the ratio of two: themeters per second.
⎡ ⎢ ⎣  metro  =  metro  ⎤ ⎥ ⎦ 
s  s 
Outside of scientific and academic circles, this unit is rarely used. Most people on this planet measure speeds inKilometers per hour(km/h or km/h). The United States is an exception in that we use the oldermile per hour(km/h or mph). Let's determine the conversion factors to be able to relate the speeds measured in m/s with the most common units.
1 km/h =  1km  1000m  1 hour  
1 hour  1km  3600er  
1 km/h =  0,2777…m/s≈¼m/s  
1 kilometer per hour =  1 for us  1609m  1 hour  
1 hour  1 for us  3600er  
1 kilometer per hour =  0,4469…m/s≈½m/s  
The decimal values shown above are accurate to four significant digits, but fractional values should only be considered as a general rule of thumb (1 km/h is really more like^{2}_{7}m/s too^{1}_{4}m/s and 1 mph is more like that^{4}_{9}m/s too^{1}_{2}Mrs).
The ratio of any unit of distance to any unit of time is a unit of speed.
 The speeds of ships, planes, and missiles are often given innode. a knot is onenautical mile per hour— a nautical mile is 1852 m or 6076 feet and an hour is 3600s. NASA still reports the speed of its rockets in knots and their range in nautical miles. A knot is approximately 0.5144 m/s.
 The slowest speeds are measured over the longest periods of time. Continental plates creep across the earth's surface at a geologically slow rate of 110cm/yearo 110m/century almost as fast as nails and hair grow.
 Audio cassettes run at 1⅞inches per second(P.S). When magnetic tape was invented, it was wound on open reels like film. These early reeltoreel tape recorders ran the tape at 15 ips. Later models could also record at half that speed (7½ ips) then half (3¾ ips) then half (1⅞ ips). When formulating the audio cassette standard, it was decided that the last of these values would suffice for the new medium. By definition, one inch per second is exactly 0.0254 m/s.
Sometimes the speed of an object is described in relation to the speed of something else; preferably some physical phenomenon.
 Aerodynamics is the study of moving air and how objects interact with it. In this area, the speed of an object is often measured relative to that object.Speed of sound. This relationship is known asmachine number. The speed of sound is about 295 m/s (660 mph) at the altitude at which commercial airliners normally fly. The nowdefunct British Airways and Air France supersonic Concorde flew at 600 m/s (1,340 mph). Simple division shows that this speed is about twice the speed of sound, or Mach 2.0, which is exceptionally fast. By comparison, a Boeing 777 flies at 555 mph (248 m/s), or Mach 0.8, which seems slow compared to the Concorde.
 Whatspeed of light in vacuumit is defined in the SI system as 299 792 458 m/s (about a billion km/h). This is usually specified to a more reasonable precision than 3.00 × 10^{8}Woman. The symbol is assigned to the speed of light in a vacuum.C(italics) when used in an equation and c (roman) when used as a unit. The speed of light in a vacuum is a universal limit, so real objects always move slower thanC. It is commonly used in particle physics and distant object astronomy. The most distant objects observed are quasars; Abbreviation for "quasistellar radio objects." They look like stars (the prefix means similar), but they radiate much more energy than any star. They are at the limits of the observable universe and are receding from us at incredible speeds. The most distant quasars recede from us at almost 0.9 °C. By the way, the iconCwas chosen not because the speed of light is a universal constant (which it is), but because it is the first letter of the Latin word for velocity:speed.
Mrs  kilometers per hour  device, event, phenomenon, process 

10^{−9}~10^{−8}  Continental plates, hair growth, nail growth  
10^{−4}  human sperm  
10^{−3}  Snails  
0,013  0,045  Pouring ketchup from a bottle 
10^{−1}  sloths, tortoises, tortoises  
0,65–1,29  2,34–4,64  cockroaches 
1  3.6  Nerve impulses, myelinated cells 
1  3.6  ocean currents 
0,06–1,14  0,22–4,10  That 
1.3  4.8  human, typical walking pace 
2.391  8.608  fastest person: swim (Cesar Himmel) 
8  30  maximum comfortable elevator speed 
10  40  dolphins, porpoises, whales 
10  40  raindrops falling 
10.422  37.520  fastest person: run (Usain Bolt) 
12  43  stadium wave 
12  44  Sektkorken 
15.223  54.803  fastest person: skating (Pavel Kulizhnikov) 
20  70  Rabbits, hares, horses, greyhounds, tunas, sharks 
30  100  typical highway speed limit 
33  118  cheetahs 
34.42  123.9  Fastest Human: Softball Court (Monica Abbott) 
40  140  hail fall 
42.47  152.9  Fastest Human: Frisbee Toss (Simon Lizotte) 
46,98  169.1  Fastest Human: Baseball Field (Aroldis Chapman) 
55  200  Terminal velocity of a typical skydiver 
70.8217  254.958  fastest person: skiing (john of oregon) 
73.06  263  fastest person: tennis serve (sam groth) 
80  290  swooping peregrine falcon 
82  295  very fast golf ball 
82.211  296,00  fastest person: cycling (Denise Korenek Muller) 
33–83  120–300  Hurricane maximum sustained wind speed 
30–90  105–330  Tornado, maximum sustained wind speed 
100  360  Nerve impulses, myelinated cells 
113.2  407.5  Maximum surface wind gust (Isla Barrow, Australia) 
118.3  426  Fastest Human: Badminton Smash (Mads Pieler Kolding) 
124.22  447.19  fastest street legal car (Konigsegg Agera RS) 
142,89  511.11  faster ship (australian spirit) 
159.7  574,8  faster train (highspeed train) 
168.249  605.697  fastest motorcycle (Top 1 Recon Attacks) 
200  700  tsunami 
250  900  airliner 
331  1.190  Speed of Sound in Air, STP 
340  1.225  speed of sound in air, sea level 
341.4031  1.229.051  fastest test car (pushSSC) 
343  1.235  Speed of sound in air, ambient temperature 
377.1  1.357,6  fastest human: skydiving (Félix Baumgartner) 
980.433  3.529,56  fastest plane (SR71 Amsel) 
180–1.200  650–4.400  pellets 
1.500  5.400  speed of sound in water 
2.000  6.000  seismic wells 
6.900  25.000  TNT detonation speed 
8.000  29.000  orbiting space shuttle 
11.094  39.938  fastest manned spacecraft (apollo 10) 
11.180  40.250  escape velocity at the earth's surface 
13.790  49.600  New Horizonsspace probe 
15.400  55.400  Voyager2space probe 
17.000  61.200  Voyager1space probe 
29.790  107.200  earth in orbit 
201.000  724.000  fastest unmanned spacecraft (probe solar parker) 
248.000  892.000  The sun moves through the Milky Way 
300.000  1.100.000  solar wind near earth 
370.000  1.330.000  Milky Way through the cosmic microwave background 
60.000.000  216.000.000  Proyecto Starshot, proposed interstellar spacecraft 
124.000.000  446.000.000  speed of light in diamond 
225.000.000  810.000.000  speed of light in water 
299.792.369  1.079.252.530  protons and antiprotons in theTevatron, Fermilab 
299.792.455  1.079.252.840  protons in theLarge Hadron Collider, CERN 
299.792.458  1.079.252.850  speed of light in vacuum 