Speed converter

Bobby Brown

Post 2022-08-23

Speed converter

Steps：Chose convert units ➜ Fill in numbers

About Speed

In everyday life, "Speed" and "Velocity" are often used interchangeably, but they represent different concepts in physics:
• Speed is a scalar quantity, meaning it only has magnitude and no direction. It is calculated by dividing the distance traveled by the time taken. For example, if a car is traveling at 60 kilometers per hour, the 60 kilometers per hour is the speed.

• Velocity is a vector quantity, meaning it has both magnitude and direction. It is calculated by dividing displacement by time. For example, if a car is traveling north at 60 kilometers per hour, the 60 kilometers per hour north is the velocity.

An object's instantaneous speed is equal to the magnitude of its instantaneous velocity, but the average speed may not equal the average velocity.

In the International System of Units (SI), the unit for speed is meters per second (m/s), though in everyday life, units like kilometers per hour (km/h) or miles per hour (mph) are more commonly used. For maritime vessels or objects, speed is typically measured in "knots" (nautical mile per hour).
According to special relativity, the maximum speed at which energy or information can travel is the speed of light in a vacuum, approximately 299,792,458 meters per second.

Definition

In mathematical language, the average speed (denoted as

\overset{ˉ}{�}

) of an object moving a distance

�

over a period

�

is the ratio of

�

�

, given by the formula:：

{\bar {v}}={\frac {s}{t}}

For example, if a car travels 60 kilometers in 2 hours, its average speed during this time is 30 kilometers per hour. The rate of an object at a specific moment is determined by the ratio of the distance

ds

與traveled in a very short time

dt

around that moment.：

v={\frac {ds}{dt}}

To precisely define it, if the distance

�

is a function of time

�

, then the instantaneous speed at a moment

t_{0}

is the limit of the above ratio as

dt

approaches zero, which mathematically means it's the derivative of

s

with respect to

�

t

t_{0}

v_{{t_{0}}}=\left.\lim _{{dt\to 0}}{\frac {ds}{dt}}\right|_{{t=t_{0}}}=\left.{\frac {{\mathrm {d}}s}{{\mathrm {d}}t}}\right|_{{t=t_{0}}}

In some simplified physical models, the rate of an object before a specific moment

v_{t_{0}}^{-}

may not equal its rate after that moment

v_{t_{0}}^{+}

：

v_{{t_{0}}}^{-}=\left.\lim _{{dt\to 0}}{\frac {s(t)-s(t-dt)}{dt}}\right|_{{t=t_{0}}}\neq \left.\lim _{{dt\to 0}}{\frac {s(t+dt)-s(t)}{dt}}\right|_{{t=t_{0}}}=v_{{t_{0}}}^{+}

For instance, in simple collision models, the velocity before and after the impact differs, highlighting discontinuities in rate changes that classical physics, which assumes continuous motion, doesn't account for. Instantaneous rate equals the magnitude of instantaneous speed, but average rate often doesn't equal average speed due to the distinction between path and displacement. For example, in uniform circular motion, the average rate is nonzero, but average speed is zero, illustrating the nuances in defining motion parameters.

Units for measuring speed include:

Meters per second (m/s), the SI derived unit
Kilometers per hour (km/h)
Miles per hour (mph)
Knots (nautical miles per hour, kt)
Mach, calculated by dividing speed by the speed of sound.
The speed of light in a vacuum (c = 2.99792458 x 10^8 m/s), a fundamental constant.

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Reference

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