Velocity and Velocity: The Hypertext of Physics (2023)

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.

☞ 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...

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...

The bar above itvindicates an average or mean and the∆The symbol (Delta) indicates a change. Read it as "V-bar is delta-ess over delta-tee". 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...

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 displacement-time 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.

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.

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.

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.

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 like²₇m/s too¹₄m/s and 1 mph is more like that⁴₉m/s too¹₂Mrs).

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 1-10cm/yearo 1-10m/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 reel-to-reel 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 now-defunct 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 × 10⁸Woman. 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 "quasi-stellar 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.