Leah here from leah4sci.com/MCAT and in this video
I'm going to show you how you can quickly
and easily determine which Kinematic equation
to use which faced with an MCAT Physics problem.
For detailed tutorials on the individual topics
and concepts including work to practice problems,
catch my entire series on translational motion
by visiting my website http://leah4sci.com/MCATPHYSICS
.
You may see many different forms of the kinematic
equations but if you understand them and work
through them you'll recognize that these are
the four main equations that you have to know.
For detailed breakdown on these equations
and more, grab my MCAT Kinematic Cheat Sheet
on my website http://leah4sci.com/MCATPHYSICS.
So let's go through them one at a time to
show you how you can rewrite them and understand
the different forms of the same question that
you'll see. Starting with the first one, notice
that we have X final is equal to X initial plus vt. If your problem starts at X equals zero,
you may drop the x and simply have the form
X is equal to vt.
You may also see this written as x is equal
to V average times t. Say we want to take
the average of A and B. We'll have A plus
B over two and that'll be the average. To
find the average velocity, we'll have Velocity
1 plus Velocity 2 over 2 and that'll give
us our V average.
Assuming you have no acceleration in the X
direction, your V1 and V2 should be the same
and therefore your V average is your Velocity.
The next equation we'll look at is V final
equal V initial plus vt. This actually comes
from the equation for Acceleration, because
Acceleration is equals to the change in Velocity
over the change in time or simply t. At delta
means the change for final minus initial and
that comes from the formula Acceleration is
equal to V final minus V initial over t. if
we wanna isolate V final from this equation,
we'll multiply both sides by t and then we
add V initial to the other side.
Rewriting this equation we get V final is
equal to V initial plus at. In this situation,
if you're starting at a velocity of zero,
velocity drops out and that gives us the simplified
version, V final is equal to at where you
may also see this simply as V is equal to
at. V being the v final.
The next equation I wanna look at is V final
squared is equal to V initial squared plus
2 a delta x. For this equation delta x is
your total displacement so you can also write
it as 2a times X final minus X initial. When
you find that change in X, you get a distance
so sometimes you'll see this equation incorrectly
written with a d, where the d represents the
distance which implies your displacement.
Once again if your initial velocity is zero,
that drops out giving you a simplified version
of the equation, V final squared is equal
to 2a delta x or even more simplified, V squared
is equal to 2ad. I don't like this form of
the equation, I especially don't like when
we're not specifying V final but you may see
it this way. To recognize that it is the same
thing.
And last but not the least, the equation that
seems to cause the most confusion is Delta
x is equal to V initial t plus one over 2at
squared. There are many ways to represent
this equation and while they say the same
thing because they don't look the same, a
lot of students get confused.
So I wanna show you how to relate the different
forms to make sure you don't get confused
if you see this on your MCAT. The first confusion
comes from the way this format the expression
is written. V sub I means V intial, V sub
f is V final, but there's another way to write
this. If you have V with a little zero that's
V not or the starting Velocity which is the
same thing as the initial velocity. So I write
this as V not t, I'm talking about the same
expression.
Another point of confusion is the X value.
Delta X means X final minus X initial, so
if I rewrite this as X final minus X initial
and then I want to solve for just X final,
I have to bring X initial over to the other
side. So do plus X initial for both sides
and rewrite the equation as follows; X final
or simply X is equal to my X initial plus
V initial t plus one over two at squared.
This is just the longer way to write it and
most likely if you're working through an MCAT
question where you're given Velocity and Acceleration,
we're assuming that you start at X equal zero
and that drops out of the equation.
And finally one more point of confusion is
that half. I've often seen the equation written
as X is equal to V initial t plus at squared
over two. This throws up a lot of students.
Anytime you have a value or an equation over
a number meaning divided by a number, you
can pull that number out and multiply it just
by one over two, in this case which is how
we get the one half a t squared.
So hopefully now you understand how to relate
the different versions of the equations which
brings up the next question, how do you know
which equation to use in any given problem?
I want you to analyze these equations with
me and recognize that we have 4 main units
that we're looking for.
Anytime we have a final and initial, we're
only looking for the final. So we have a unit
for X or displacement, we have a unit for
Velocity specifically V final. We have a unit
for Acceleration and we have Time. Every equation
given has three out of the four units. The
first one has X V and T but it does not have
Acceleration. The second one has V final,
we're ignoring V initial a and t but it does
not have displacement or X.
The third one has V final, it has Acceleration
and displacement but it does not have time.
And finally the last one has displacement,
we're ignoring V initial remember we're looking
for V final as our unit. We have acceleration,
we have time, we do not have velocity final.
In referring to these equations we can say
it has the three given or we can it is missing
so for example the first equation is the acceleration
independent equation, the second one is displacement
independent and so on.
Anytime you're given a Kinematic question
you'll be provided with two units and ask
to solve for the third. So the way you can
tell which equation to use is identify the
two units that you're given, the unit that
you're asked to solve and then see which equation
has those three units. So for example, if
I tell you to solve for the total distance
and I give velocity and time, I'll see that
I'm asked for distance, I'm given Velocity
and time but I'm not given Acceleration or
told to solve for Acceleration. So why would
I consider unit that I really have no use
for.
In that situation we solve for the acceleration
independent equation. Now one thing I want
you to keep in mind, everything here is written
out for the X component but if you the Y,
you can swap it out. X becomes Y and acceleration
becomes the acceleration of gravity at ten
meters per second squared. Keeping all this
in mind, I want you to go back to my Kinematic
Videos where I walk you through examples of
Velocity displacement, acceleration, freefall,
projectile motion and I want you to consider
the individual problems and see how I determined
what we're given, what we're asked for, what
we're not asked for and therefore quickly
narrow down the equation to use. You can find
my entire series on Translational Motion by
visiting my website http://leah4sci.com/MCATPHYSICS.
Are you stuck on a specific MCAT topic? I
offer Private Online Tutoring where I focus
on your needs to strengthen your individual
weaknesses. Tutoring details can be found
using the link below or by visiting my website
leah4sci.com/MCATTutor.
Are you overwhelmed by the sheer volume of
information required for the MCAT? Are you
worried that lack of a proper study plan and
low MCAT score will prevent you from getting
into Medical School? My new eBook The MCAT
Exam Strategy is 6-Week Guide to Crushing
the MCAT will help you formulate a concrete
study plan by helping you figure out where
you stand now, identify your goals and figure
out what it takes to reach them and it's yours
FREE when you sign up for my email newsletter
at McatExamStrategy.com. By signing up for
my email newsletter, you'll also be the first
to know when I have new videos, MCAT Study
Guide Cheat Sheets, Tips and so much more!
The link again McatExamStrategy.com
