Hey it's professor Dave, let's discuss
position, velocity, and acceleration.
In physics, we will
often be asking questions like where is
an object, which way is it moving, and how
fast? To discuss the answers to these
questions we will frequently utilize the
concepts of position, velocity, and
acceleration. So before we go any further
let's define these terms. Position is
simple, it's just where an object is in
space. Usually this is discussed with
some kind of reference point or axes in
mind, and we might express the position
of an object as being some distance from
this reference point in meters. Velocity
is the change in position over time, so
if this object travels five meters in
five seconds it is traveling at a
velocity of one meter per second. And
acceleration is the change in velocity
over time, so if this object starts at a
standstill and over five seconds
gradually speeds up to 5 meters per
second, then it is accelerating at one
meter per second per second, or 1 meter
per second squared. So that's how we
define position, velocity, and
acceleration. Now let's discuss each of
these in more depth. When we talk about
position we could discuss distance or we
could discuss displacement. The
difference here is that distance is a
scalar while displacement is a vector.
Let's say you and your friend get
dropped off by the school bus at this
intersection and your house is here. Your
friend begins to walk down the street
and up the driveway like a normal person
but you find yourself so overcome with
excitement to play video games that you
decide to plow through the yard in a
straight line to the door.
Your friend has to walk 20 meters down
the street and seven meters up the
driveway for a total of twenty seven
meters, so using the Pythagorean theorem
we find that you only had to walk about
21.2 meters
and you probably got there a little
sooner. What we can say is that you
walked different distances, which are
represented by these scalar values, but
you both had the same displacement
because you ended up in the same spot at
the front door. This vector which follows
the straight-line path is the
displacement vector for both of you and
we can report your position with x and
y-coordinates like this
(20, 7) or we could report the
magnitude of the displacement vector
which will be equal to the shorter
distance you traveled and calculate the
angle off the horizontal using trig
functions if we desire, in order to
report the direction of the vector. Next
let's look at velocity which is the rate
of change in position.
Most people assume that the words speed
and velocity are synonyms and in
everyday language they are, but the
difference in physics is that speed is a
scalar and velocity is a vector. If a
group of kids are playing hide-and-seek
and they all run away from the seeker in
different directions
it is possible that they all run at the
same speed because speed only has
magnitude and no direction so they could
all run at a speed of three meters per
second if they are quick little devils
but each kid would have a unique
velocity vector that has a magnitude of
three but also describes the direction
of motion, most likely using the seeker
standing still as the point of origin.
Velocity vectors will be extremely
important as we move forward with
kinematics where we will study the
motion of objects. In general, average
speed can be calculated by taking the
distance travelled by an object and
dividing by the time it took to do so,
so if you walk 85 meters in 46 seconds
you are walking at an average speed of
1.85 meters per second. To find average
velocity you can do the same but you
would have to divide displacement by time.
Lastly we have acceleration, which is the
rate of change in velocity. This is
always a vector,
because acceleration must occur in a
particular direction. If you are in a car
that is standing still and you press on
the gas, the car will begin to move
forward with a fixed acceleration. It
might accelerate slowly so the vector
may be on the shorter side, but this
constant acceleration will cause the
velocity to increase at a fixed rate,
let's say an additional meter per second
every second, so over five seconds it
will reach a velocity of 5 m/s. Let's say
you see a skunk in the middle of the road.
It's your most favorite animal so you
slam on the brakes. We can describe this
as a deceleration, which is an
acceleration in the negative direction.
Since you are going from a moderate
speed to a standstill in a very short
amount of time this vector will be quite
long and pointing back towards the
origin. Now we understand distance and
displacement, speed and velocity, and
acceleration, and we can categorize these
as being either scalars or vectors.
Before we finish let's look at a moving
object like this marble rolling to a
stop and visualize all three of these
vectors as the object moves. First with
displacement this vector will just
elongate as the marble rolls and will
span the distance travelled. For velocity
the vector will point forward as the
velocity is positive, since it is moving
in the forward direction, and the vector
will move along with the marble but it
will decrease in magnitude as the marble
slows down until eventually disappearing
when the marble comes to a rest, where it
has zero velocity. And then for
acceleration the vector points in the
negative direction since velocity is
decreasing or becoming smaller per unit
time but it will be constant in
magnitude since this is a constant
deceleration due to friction from the
surface it's rolling on. We can view all
three of these at once just to drive
things home. Make sure you understand the
magnitude and direction of each of these
vectors at each moment in time.
Let's check comprehension.
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