# Motion: Speed, Velocity, Acceleration (Module 1.02, 1.03)

• a link to a quizlet
• some useful notes about speed, velocity, and acceleration
• and a host of (possibly) helpful websites

…just keep paging down, you’ll find things.  🙂

# Some definitions

Remember, speed = distance / time.

Velocity = displacement / time.

The difference between distance and displacement:  distance is the ground covered, and displacement is your finishing point – your starting point.  So if you go around a standard HS track once, your distance is 1/4 mile.  But your displacement from start to finish is 0–zero!

Remember, velocity is a vector quantity–that is, it is associated with direction.  The same is true with displacement.  Distance, however, is a scalar quantity–it has only magnitude, not direction (and therefore cannot be negative.)

Also remember, acceleration = change in velocity / time.

You can have a positive velocity–you are moving forward–but if you are at the same time slowing down, then you are at decelerating (negative acceleration, positive velocity).

You can also have a negative velocity–that means you are going backward (or in whichever direction is the opposite of the direction that you’ve identified as positive).  It also means that you could be driving a car backward, start at a velocity of -5 miles per hours (negative because there is a direction associated with velocity, and you are going backward), and increase your speed to 20 miles per hours (but still going backward, so velocity is -20 mph).  That would mean a change in velocity of

V-final – V-intial = -20 – -5 = -20 + 5 = -15.

And THAT would mean that you have a negative acceleration–even though you are speeding up, you are moving further and further away (at a faster rate) from traveling in a positive direction.

Imagine, though, that you started at -15 as your initial speed, and finished at 0 as your final speed.  then your would have

0 – -15 = 15

as your acceleration.  You would be positively accelerating, because even though you were slowing down, you were going slower in a backward direction–and eventually stopped.  As you were going slower in a backward direction, you were getting closer to going in a positive direction!

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Fun fact:  “escape velocity” is the term for the velocity necessary for someone or something (say, a rocket) to escape the gravitational pull of the earth.

The gravitational pull of the earth causes things in free-fall (that is, objects that have only gravity acting on them as a force) fall at 9.8 meters per second squared.  Here is the famous moon drop experiment, which shows that ALL things that are dropped (that is, they start with a velocity of 0) all fall at the same rate.

In reality, of course, on eath, things don’t fall quite at 9.8 meters per second-squared–primarily because of air resistance, which is sort of like friction–it acts against the dfalling motion downward.

The graphs on the left represent various ways to depict motion.

There are three types of graphs.  Each row starts off with a position-time graph.  Then, to the right of the position-time period, there is a velocity-time graph.    And then, to the right of the velocity-time graph, there is a acceleration-time period.

Consider the first option:  an object that is not moving.  It has a position–it is located somewhere–but its position doesn’t change.  That is what that first position-time graph (top left) shows you.

Then look at the corresponding velocity-time graph, on the right.  The velocity is 0–so the line is drawn along the x access.  The velocity is also not changing, so there is no acceleration, so the acceleration-time graph also has a line drawn along the x-axis.

Consider the next row, the middle row.  The object is moving now, at a constant velocity–its position is changing.  But even though it has a velocity (it is moving), the velocity is constant.  Therefore the velocity-time graph represents a positive but constant (flat slope–no change in velocity) velocity.  And since there’s no change in velocity, the acceleration is still 0–which means a flat line along the x axis.

Consider the last row of graphs–depicting an object that is accelerating (constant acceleration).  In this case, it is accelerating in a positive direction.  The position is changing–at an ever increasing rate, because the object is speeding up.  The velocity is positive and increasing.  And the acceleration is constant, but it is positive.

A couple of excellent websites:

A useful video on the difference between velocity and speed Remember, velocity is the displacement divided by time, whereas speed is distance divided by time.  Velocity has direction associated with it[m  (east, west, north, south, up, down, left, right, forward, backward, etc.)  Speed is the absolute value of velocity; it is always positive.  Here is an video with an example problem about velocity and speed.

Here is a video about thinking about position v. time graphs, as related to walking.

And a video discussing instantaneous versus average velocity.

A video discussion throwing up the ball in the air, and how the velocity changes.  And here’s the follow-up video about dropping a ball, and throwing a ball up in the air, as well as one using time-stop photography to create a position time graph.

A really good video on conversions It goes a little further than physical science students need in terms of significant digits, and is really designed for physics students, but it’s pretty good nonetheless.

A really good video on accuracy and precision.  These two concepts seem to be key concepts in science and math throughout at least middle (and possibly elementary) school through high school.

A couple of excellent websites:

A useful video on the difference between velocity and speed Remember, velocity is the displacement divided by time, whereas speed is distance divided by time.  Velocity has direction associated with it[m  (east, west, north, south, up, down, left, right, forward, backward, etc.)  Speed is the absolute value of velocity; it is always positive.  Here is an video with an example problem about velocity and speed.

Here is a video about thinking about position v. time graphs, as related to walking.

And a video discussing instantaneous versus average velocity.

A video discussion throwing up the ball in the air, and how the velocity changes.  And here’s the follow-up video about dropping a ball, and throwing a ball up in the air, as well as one using time-stop photography to create a position time graph.

A really good video on conversions It goes a little further than physical science students need in terms of significant digits, and is really designed for physics students, but it’s pretty good nonetheless.

A really good video on accuracy and precision.  These two concepts seem to be key concepts in science and math throughout at least middle (and possibly elementary) school through high school.