How to find velocity?

Answer 1

Simple Answer

Velocity is a vector quantity, so you need to express velocity in terms of both speed and direction.

.

The simple (but incomplete) answer is to divide the distance over time in the direction travelled. For example, 25 miles per hour north is a velocity.

.

This answer is suitable for at least 99% of everyday life situations.

More Complete Answer

The scientifically accurate (but long) answer is actually quite complicated. Note this description does not apply to measuring the velocity of light. And remember, velocity must always be expressed as both speed and direction.

.

Speed (distance over time) is always measured with respect to an arbitrary point of reference - speed is never absolute. For common purposes, most people either use themselves or the ground as an arbitrary local point of reference. For example, a car said to be travelling at 100 kilometers per hour is travelling that speed with respect to the ground. The ground is the arbitrary local reference point. In another example, a boy on a moving train throws a ball down the isle at 10 miles per hour. The speed is expressed relative to the boy, but if the train is travelling 50 miles per hour relative to the ground, then the ball travels at either 40 mph or 60 mph relative to the ground, depending upon which direction the boy threw the ball.

.

Speed can be expressed relative to another moving object (technically all objects move). For example, you could say that two jet aircraft flying head-on in a collision course are closing at a speed of 1,800 km/h. In this case, each aircraft uses the other aircraft as the arbitrary local reference point.

.

Expressing speed becomes more difficult when there are no easy arbitrary reference points. For example, how do you express the speed of a space probe travelling from Earth to Jupiter? You might think using the ground you are standing on as the arbitrary reference point makes sense, but in fact that proves to be utterly useless. Consider that the equatorial surface of the planet Earth spins around at a speed of 1,667 kilometers per hour with respect to the earth's rotational axis. So the speed of the space probe, using an arbitrary point on the Earth's surface as a reference point, changes dramatically from daytime to nighttime, when at one moment the ground you are standing on is spinning toward the probe, and in the other moment you are receding from the probe, with a net difference of over 3,200 km/hr. So why not use the Earth's center as the reference point? To further complicate the issue, in the summer/fall, the earth might fly away from the probe in its orbit around the sun, and in the winter/spring, the earth could be racing toward the probe (the seasons could be different - I am just using these seasons as an example). The earth orbits around the Sun at a speed of 106,700 km/hr with respect to the Sun, so the speed of the probe with respect to the center of Earth changes by over 200,000 km/hr from winter to summer. There must be a better way.

.

In the case of the space probe, the center of the sun is the best arbitrary reference point. That is why space operators launch probes at a time of year when the planet Earth is closing toward the destination point at its fastest relative speed - because the space probe gains orders of magnitude more speed from the earth's orbital speed around the sun than the probe could hope to gain from its own rocket engines. If the space probe were to leave our solar system and visit other worlds, even our Sun would no longer be a useful arbitrary point of reference, as explained below.

.

Direction is always expressed with respect to an arbitrary frame of reference. For example, you could say the direction is up, north, towards the sun, or counterclockwise. Changing the frame of reference changes your understanding of direction. For example, someone pointing 'up' in Tokyo is pointing to a completely different cluster of stars than someone pointing 'up' at the same moment while standing in Paris. The direction 'north' is the same for all points on the earth only when standing exactly on the equator. At the exact south pole, you could point in any and all direction (save directly 'up') and you would be pointing north. The concept of clockwise depends upon from which side you view the clock.

.

When velocity is expressed in local terms - that is, when the frame of reference does not extend beyond about 100 km - then the usual terms for direction (north, up, etc.) suffice. But as soon as velocity is expressed in a context that considers more than a few hundred kilometers, the terms 'north', 'up', etc. begin to lose their usefulness as a reliable expression of direction. In astronomy, directions are most commonly expressed with respect to the center and ecliptic plane of the solar system or of the galaxy, known as the ecliptic coordinate system and galactic coordinate system, respectively.

.

Velocity does not need to be a linear value. For example, the angular (rotational) velocity of a merry-go-round can be expressed as 0.3 radians per second clockwise when viewed from above. Similarly, the Earth can be said to rotate at an angular velocity of 15o per hour counterclockwise when viewed from the star Polaris.

.

In conclusion, velocity is distance, or angular displacement, over time in a specific direction with reference to an arbitrary frame of reference. You must understand that frame of reference to correctly interpret the intended meaning of the expressed velocity.