What is velocity?

The meaning of velocity

Intro to the mathematics of motion

Today, we are going to talk about how we think about speed and the rate of change in speed (usually called acceleration).  It is a bit math-y, but don't panic - we'll summarize things nicely in a couple of simple-to-use equations.

First, let's look at some definitions.

Average (or constant) velocity, v

v = d / t

That is, distance divided by time.  The SI units are meters per second (m/s).

* Strictly speaking, we are talking about speed, unless the distance is a straight-line and the direction is also specified (in which case "velocity" is the appropriate word).  However, we'll often use the words speed and velocity interchangeably if the motion is all in one direction (1D).


Some velocities to ponder....

Approximately....

Keep in mind that 1 m/s is approximately 2 miles/hour.

Your walking speed to class - 1-2 m/s
Running speed - 5-7 m/s
Car speed (highway) - 30 m/s
Professional baseball throwing speed - 45 m/s
Terminal velocity of skydiver - 55 m/s
Speed skiing - 60 m/s
Speed of sound (in air) - 340 m/s
Bullet speed (typical) - 900 m/s
Satellite speed (in orbit) - 6200 m/s
Escape velocity of Earth - 11,200 m/s
(That's around 7 miles per second, or 11.2 km/s)


What about.....
The Speed of light

Speed of light (in a vacuum) -

c = 299,792,458 m/s


This number is a physical constant, believed to be true everywhere in the universe. The letter c is used to represent the value being of constant celerity (speed).

By the way, it's hard to remember this exact number, and I wouldn't expect you to.  However, here are some approximations that may make it easier to keep it in mind.  The speed of light is approximately:

- 300,000,000 meters/sec

- 186,000 miles/sec

- 7 times around the Earth's equator in 1 second

- Out to the Moon in around 1 second (1.3 seconds is closer) - so, the Moon is approximately 1.3 "light seconds" away (on average)

- To the Sun in about 8 minutes - so, the Sun is approximately 8 "light-minutes" away (on average)

- To Mars in about 13 minutes, though this varies depending on the relative locations of Earth and Mars in their respective orbits.  (Consider that this is, under the best circumstances, about a 9 month one-way trip at current spaceship speeds.)

- To the nearest (non-Sun) star, Proxima Centauri B (actually part of a 3-star system, and home to a recently-discovered Earth-like planet!), in 4.24 years.  Yes, YEARS.  So, that 3-star system is around 4.3 "light years" away from us.  And that's our closest neighbors!!  See why we don't get too far in space travel?


Instantaneous Velocity

Average velocity should be distinguished from instantaneous velocity (what you get, more or less, from a speedometer):

v(inst) = d / t, where t is a very, very, very tiny time interval. There's more to be said about this sort of thing, and that's where calculus begins.

Now the idea of velocity is pretty useful if you care about the velocity at a specific time OR the average velocity for a trip. However, if you care about the details of velocity, if and when it changes, then we need to introduce a new concept: acceleration.

Comments

Post a Comment

Popular posts from this blog

Newton's take on Gravitation - the inverse square law

Image
Newton's take on gravity and orbits - which is the genesis of our modern conception of it, is based on: Universal Gravitation (1687, Principia) Newton's take on orbits was quite different. For him, Kepler's laws were a manifestation of the bigger "truth" of universal gravitation. That is: All bodies have gravity unto them. Not just the Earth and Sun and planets, but ALL bodies (including YOU). Of course, the gravity for all of these is not equal. Far from it. The force of gravity can be summarized in an equation: or.... the force of gravitation is equal to a constant ("big G") times the product of the masses, divided by the distance between them (between their centers, to be precise) squared. Big G = 6.67 x 10^-11, which is a tiny number - therefore, you need BIG masses to see appreciable gravitational forces. This is an INVERSE SQUARE law, meaning that: - if the distance between the bodies is doubled, the force becomes 1/4 of its ...
Read more

Lenses and how they form images

Image
Lenses As shown and discussed in class, light refracts TOWARD a normal line (dotted line on the left image, perpendicular to surface of lens) when entering a more dense medium. Note in this  convex  lens that this direction of bend changes from down (with the top ray) to up with the bottom ray. This is due to the geometry of the lens. Look at the picture to make sure that this makes sense.  As a result, the rays will intersect after leaving the lens.  An image can form! The FOCAL LENGTH (f) of a lens (or curved mirror) where the light rays would intersect, but ONLY IF THEY WERE INITIALLY PARALLEL to each other. Otherwise, they intersect at some other point, or maybe not at all (if the object is too close to be focused on)! Note that your (human) eye lenses are convex - slightly thicker in the middle.  Thus, your eyes form "real" images on the retina - upside-down!  Unless, of course, the object is too close. If an image is projected onto ...
Read more

Electromagnetism and Electromagnetic Induction

Image
Electromagnetism Recall that the motion of charges leads to magnetic fields.   If you have charge traveling through a wire, electrons can be thought of as moving together – this causes a magnetic field, also known as electromagnetism.  The magnetic field caused by a current passing through a wire is often small, but if you coil the wire upon itself, the magnetic fields “add up”.  Several hundred turns of wire (with current running through it) can produced quite a strong electromagnet.  A coil with current running through it can naturally react to a permanent magnet – if this is engineered well, we have a motor.  See illustrations and demos in class. Below:  basic motors Electromagnetic Induction So, current causes magnetism – something shown in the early 19 th  century by Hans Oersted.  As it happens, the reverse is also true – magnetism can cause current, but there must be some relative CH...
Read more