what is the correct way to calculate the speed of an object
Speed and Velocity
Give-and-take
speed
What'southward the deviation between two identical objects traveling at different speeds? Virtually everyone knows that the one moving faster (the one with the greater speed) will go farther than the one moving slower in the same amount of fourth dimension. Either that or they'll tell you lot that the i moving faster will go where it's going sooner than the slower i. Whatsoever speed is, it involves both distance and time. "Faster" means either "farther" (greater distance) or "sooner" (less time).
Doubling 1's speed would mean doubling one'south distance traveled in a given corporeality of time. Doubling ane's speed would too mean halving the time required to travel a given distance. If you know a little well-nigh mathematics, these statements are meaningful and useful. (The symbol v is used for speed because of the association between speed and velocity, which will be discussed shortly.)
- Speed is direct proportional to distance when time is constant: v ∝southward (t constant)
- Speed is inversely proportional to time when altitude is abiding: v ∝ 1 t (s constant)
Combining these two rules together gives the definition of speed in symbolic form.
☞ This is not the last definition.
Don't similar symbols? Well and so, here's another style to define speed. Speed is the rate of change of distance with time.
In order to calculate the speed of an object nosotros must know how far it'southward gone and how long information technology took to become in that location. "Farther" and "sooner" correspond to "faster". Permit's say you collection a car from New York to Boston. The distance by road is roughly 300 km (200 miles). If the trip takes four hours, what was your speed? Applying the formula above gives…
| v = | south | ≈ | 300 km | = 75 km/h |
| t | 4 hour |
This is the answer the equation gives united states of america, simply how right is it? Was 75 kph the speed of the machine? Yes, of course it was… Well, maybe, I guess… No, information technology couldn't accept been the speed. Unless you live in a globe where cars have some kind of exceptional prowl control and traffic flows in some ideal manner, your speed during this hypothetical journey must certainly have varied. Thus, the number calculated in a higher place is not the speed of the car, it'south the average speed for the entire journeying. In guild to emphasize this point, the equation is sometimes modified equally follows…
The bar over the five indicates an boilerplate or a hateful and the ∆ (delta) symbol indicates a modify. Read it as "vee bar is delta ess over delta tee". This is the quantity nosotros calculated for our hypothetical trip.
In contrast, a car's speedometer shows its instantaneous speed, that is, the speed determined over a very small-scale interval of time — an instant. Ideally this interval should be as close to zero equally possible, but in reality we are limited past the sensitivity of our measuring devices. Mentally, however, it is possible to imagine calculating average speed over ever smaller time intervals until we have finer calculated instantaneous speed. This idea is written symbolically equally…
or, in the linguistic communication of calculus speed is the first derivative of altitude with respect to time.
If you haven't dealt with calculus, don't sweat this definition besides much. There are other, simpler ways to notice the instantaneous speed of a moving object. On a distance-time graph, speed corresponds to slope and thus the instantaneous speed of an object with non-constant speed can be found from the slope of a line tangent to its curve. We'll deal with that later in this book.
velocity
In order to calculate the speed of an object we demand to know how far it'southward gone and how long it took to get there. A wise person would then enquire…
What practise you mean by how far? Do you lot want the altitude or the deportation?
A wise person, once upon a time
Your option of answer to this question determines what you summate — speed or velocity.
- Boilerplate speed is the rate of modify of distance with time.
- Average velocity is the rate of change of deportation with time.
And for the calculus people out there…
- Instantaneous speed is the first derivative of distance with respect to fourth dimension.
- Instantaneous velocity is the showtime derivative of deportation with respect to fourth dimension.
Speed and velocity are related in much the same way that distance and displacement are related. Speed is a scalar and velocity is a vector. Speed gets the symbol v (italic) and velocity gets the symbol v (boldface). Average values go a bar over the symbol.
| average speed | ||
| instantaneous speed |
| average velocity | ||
| instantaneous velocity |
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 displacement approaches distance as distance approaches naught. That is, distance and displacement are finer the same (have the same magnitude) when the interval examined is "pocket-sized". Since speed is based on distance and velocity is based on displacement, these 2 quantities are effectively the same (have the same magnitude) when the fourth dimension interval is "minor" or, in the language of calculus, the magnitude of an object's average velocity approaches its boilerplate speed as the time interval approaches zero.
The instantaneous speed of an object is then the magnitude of its instantaneous velocity.
v = |v|
Speed tells yous how fast. Velocity tells you how fast and in what direction.
units
Speed and velocity are both measured using the aforementioned units. The SI unit of altitude and displacement is the meter. The SI unit of time is the second. The SI unit of speed and velocity is the ratio of two — the meter per second.
| ⎡ ⎢ ⎣ | one thousand | = | m | ⎤ ⎥ ⎦ |
| southward | s |
This unit is only rarely used outside scientific and academic circles. Most people on this planet measure speeds in kilometer per hour (km/h or kph). The U.s. is an exception in that we employ the older mile per hr (mi/h or mph). Let's determine the conversion factors so that we can relate speeds measured in thou/due south with the more familiar units.
| 1 kph = | 1 km | 1000 m | 1 60 minutes | |||
| one hour | one km | 3600 s | ||||
| 1 kph = | 0.2777… thou/southward ≈ ¼ grand/s | |||||
| 1 mph = | i mile | 1609 k | 1 hour | |||
| i hour | 1 mile | 3600 due south | ||||
| 1 mph = | 0.4469… thousand/s ≈ ½ m/south | |||||
The decimal values shown to a higher place are authentic to four meaning digits, simply the fractional values should only be considered rules of thumb (ane kph is actually more than like 2 vii m/s than i 4 m/s and one mph is more than like 4 9 m/s than 1 ii m/s).
The ratio of any unit of distance to any unit of measurement of time is a unit of speed.
- The speeds of ships, planes, and rockets are often stated in knots. One knot is one nautical mile per hour — a nautical mile existence 1852 1000 or 6076 anxiety and an hour beingness 3600 s. NASA still reports the speed of its rockets in knots and their downrange distance in nautical miles. One knot is approximately 0.5144 yard/s.
- The slowest speeds are measured over the longest time periods. The continental plates creep across the surface of the Earth at the geologically ho-hum rate of i–10cm/year or 1–10chiliad/century — nearly the same speed that fingernails and hair grow.
- Sound cassette tape travels at 1⅞ inches per 2d (ips). When magnetic tape was kickoff invented, information technology was spooled on to open up reels similar motion-picture show film. These early reel-to-reel tape recorders ran the record through at fifteen ips. Afterwards models could also record at half this speed (seven½ ips) and then half of that (3¾ ips) and and then some at half of that (1⅞ ips). When the sound cassette standard was being formulated, it was decided that the concluding of these values would exist sufficient for the new medium. One inch per second is exactly 0.0254 m/south by definition.
Sometimes, the speed of an object is described relative to the speed of something else; preferably some physical phenomenon.
- Aerodynamics is the study of moving air and how objects interact with information technology. In this field, the speed of an object is often measured relative to the speed of sound. This ratio is known as the Mach number. The speed of sound is roughly 295 yard/s (660 mph) at the altitude at which commercial jet aircraft usually fly. The now decommissioned British Airways and Air France supersonic Concorde cruised at 600 m/s (1340 mph). Simple division shows that this speed is roughly twice the speed of sound or Mach 2.0, which is exceptionally fast. A Boeing 777, in comparison, cruises at 248 1000/s (555 mph) or Mach 0.viii, which simply seems boring in comparison to the Concorde.
- The speed of light in a vacuum is divers in the SI organisation to be 299,792,458 m/s (almost a billion km/h). This is usually stated with a more than reasonable precision as 3.00 × 108 one thousand/s. The speed of light in a vacuum is assigned the symbol c (italic) when used in an equation and c (roman) when used equally a unit. The speed of light in a vacuum is a universal limit, and then real objects always move slower than c. It is used ofttimes in particle physics and the astronomy of distant objects. The virtually distant observed objects are quasars; short for "quasi-stellar radio objects". They are visually like to stars (the prefix quasi ways resembling) just emit far more energy than any star mayhap could. They lie at the edges of the observable universe and are rushing abroad from us at incredible speeds. The nigh distant quasars are moving away from us at most 0.ix c. By the mode, the symbol c was called not because the speed of light is a universal abiding (which it is) simply because it is the first alphabetic character of the Latin word for swiftness — celeritas.
| k/s | km/h | device, event, phenomenon, process |
|---|---|---|
| ten−9~10−8 | continental plates, pilus growth, fingernail growth | |
| 10−4 | human sperm cells | |
| ten−3 | snails | |
| 0.013 | 0.045 | ketchup pouring from a bottle |
| x−1 | sloths, tortoises, turtles | |
| 0.65–i.29 | 2.34–iv.64 | cockroaches |
| 1 | 3.half dozen | nerve impulses, unmyelinated cells |
| i | 3.6 | sea currents |
| 0.06–i.14 | 0.22–4.x | manatees |
| 1.3 | 4.viii | human being, typical walking stride |
| two.391 | eight.608 | fastest human: swimming (César Cielo) |
| eight | 30 | maximum comfortable elevator speed |
| ten | forty | dolphins, porpoises, whales |
| 10 | 40 | falling raindrops |
| ten.422 | 37.520 | fastest man: running (Usain Bolt) |
| 12 | 43 | stadium wave |
| 12 | 44 | champagne cork |
| fifteen.223 | 54.803 | fastest man: ice skating (Pavel Kulizhnikov) |
| twenty | 70 | rabbits, hares, horses, greyhounds, tuna, sharks |
| 30 | 100 | typical freeway speed limit |
| 33 | 118 | cheetahs |
| 34.42 | 123.9 | fastest human: softball pitch (Monica Abbott) |
| 40 | 140 | falling hailstones |
| 42.47 | 152.9 | fastest homo: flying disc throw (Simon Lizotte) |
| 46.98 | 169.1 | fastest human being: baseball pitch (Aroldis Chapman) |
| 55 | 200 | concluding velocity of a typical skydiver |
| 70.8217 | 254.958 | fastest human: skiing (Ivan Origone) |
| 73.06 | 263 | fastest man: tennis serve (Sam Groth) |
| 80 | 290 | peregrine falcon in a dive |
| 82 | 295 | very fast golf ball |
| 82.211 | 296.00 | fastest human being: cycling (Denise Korenek Mueller) |
| 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.ii | 407.5 | maximum surface wind gust (Barrow Island, Australia) |
| 118.3 | 426 | fastest homo: badminton blast (Mads Pieler Kolding) |
| 124.22 | 447.19 | fastest street-legal car (Koenigsegg Agera RS) |
| 142.89 | 511.11 | fastest ship (Spirit of Australia) |
| 159.vii | 574.8 | fastest train (Train à Grande Vitesse) |
| 168.249 | 605.697 | fastest motorcycle (Top 1 Ack Attack) |
| 200 | 700 | tsunami |
| 250 | 900 | commercial jet aeroplane |
| 331 | 1,190 | speed of audio in air, STP |
| 340 | 1,225 | speed of audio in air, sea level |
| 341.4031 | 1,229.051 | fastest experimental machine (Thrust SSC) |
| 343 | 1,235 | speed of sound in air, room temperature |
| 377.one | one,357.vi | fastest human: skydiving (Felix Baumgartner) |
| 980.433 | iii,529.56 | fastest airplane (SR-71 Blackbird) |
| 180–1,200 | 650–iv,400 | bullets |
| 1,500 | 5,400 | speed of audio in h2o |
| 2,000 | half-dozen,000 | seismic waves |
| 6,900 | 25,000 | detonation velocity of TNT |
| viii,000 | 29,000 | infinite shuttle in orbit |
| eleven,094 | 39,938 | fastest manned spacecraft (Apollo x) |
| 11,180 | twoscore,250 | escape velocity on the surface of the Earth |
| 13,900 | 50,400 | New Horizons infinite probe |
| 15,400 | 55,400 | Voyager 2 space probe |
| 17,000 | 61,200 | Voyager ane infinite probe |
| 29,790 | 107,200 | Earth in orbit |
| 190,000 | 690,000 | fastest unmanned spacecraft (Parker Solar Probe) |
| 248,000 | 892,000 | Sun moving through the Milky Way |
| 300,000 | ane,100,000 | solar wind near world |
| 370,000 | 1,330,000 | Galaxy through the cosmic microwave background |
| 60,000,000 | 216,000,000 | Projection Starshot, proposed interstellar space probe |
| 124,000,000 | 446,000,000 | speed of light in diamond |
| 225,000,000 | 810,000,000 | speed of lite in water |
| 299,792,369 | 1,079,252,530 | protons and antiprotons in the Tevatron, Fermilab |
| 299,792,455 | 1,079,252,840 | protons in the Big Hadron Collider, CERN |
| 299,792,458 | 1,079,252,850 | speed of light in a vacuum |
No status is permanent.
Source: https://physics.info/velocity/
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