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.
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