BAM!
Mr. Tarrou.
Congratulations on completing your AP Calculus AB course.
But now come the second phase of our studies which is preparing to pass that AP test.
We want that college credit to, you know, represent...
get a reward for all of that work that we have put into this class over the last many
months.
We are going to something different for me.
This is going to be...
I am going to start releasing some short form videos where we just do a couple of examples
every couple of days.
And I am going to create a playlist of all of these lessons, of course in sequence.
I am just randomly picking these problems, but I will put them in sequence as I release
them.
Now I am not going to be creating some distractors, or multiple choices, for these questions.
But they do represent or they are inspired by problems I have been using over the last
four years to get my kids ready for their AP tests.
So here we go.
Look forward to hopefully having you all watch a lot more of these and get those 5's that
you deserve like BAM!
So for an object moving in a straight line the graph represents, this graph, represents
the velocity of an object moving as a function of time.
So the x axis, if you will, is time and the vertical scale is for velocity.
At which point is the speed the greatest.
Do you remember how the speed and the velocity are related?
The second question here is at which of these points is the speed increasing.
So take a minute, try and figure it out.
I am going to come back and go over these questions, the answers.
Then I am going to summarize what I said in a nice set of notes and also make sure...
I will make sure that you have a link in the description if you want to go and look at
a full length lesson that is related to the concepts of whatever these questions happen
to be about as we go through this series of videos.
[nanananana] So at which point is the speed the greatest?
Well velocity is positive if you are moving to the right or up, and negative if you are
moving backwards or down.
So we have got some positive velocities here at point A, B, and C. And negative velocities
at point E, F, and G. Because remember the vertical scale is velocity.
But, since speed is the absolute value of velocity this value of F... this point F is
the farthest point away from this t axis if you will.
So while that might be the lowest value for velocity being negative, since speed is again
the absolute value it is going to be the answer of F.
This is when the speed is the greatest.
Like your speedometer.
The SPEEDometer in your car does not differentiate between whether you are going forward or whether
you are going backwards.
If you go forward in first gear 5 miles per hour, the speedometer says 5.
You go backwards, it is still going to say 5.
It is not going to reflect the fact that you are going in reverse.
You better be looking over your shoulder.
At which points is the speed increasing?
Well when does the speed of an object increase?
The speed of an object increases when the velocity and acceleration have the same sign.
So the velocity and acceleration have the same sign.
So S(t) is normally referred to as the position function.
So S prime of t is equal to velocity.
Ok, and this is the velocity function, right.
We were told that this graph represents the velocity, not the position of the object.
And then s double prime of t is equal to the derivative or the first derivative of velocity
which is equal to acceleration.
So we need the velocity and the acceleration to have the same sign.
Well like at point A the velocity is positive.
And since acceleration is the derivative of velocity, and this has a positive slope at
point A.. not only is the velocity is positive, so is the acceleration.
So at point A your speed is going to be increasing.
At B the acceleration is zero, because if I come in here and draw a tangent line it
is going to be horizontal.
If I come here at C and draw a tangent line representing the slope, the slope again of
velocity is the acceleration.
So we have a positive velocity, but a negative acceleration.
At this point....
At that point C this object...
its speed is going to be decreasing.
And now down here at E. At E the velocity graph is below the t axis, so the velocity
is going to be is negative.
But so is the slope.
So if the velocity and the acceleration have the same sign, then that object is picking
up speed.
And so the final answer here, as far as at what points is the speed increasing.
The speed is going to be increasing at A because you have a positive velocity and a positive
acceleration.
And at E because you have a negative velocity and a negative acceleration.
And that is the end of our first review.
Just....
I am going to walk out, pause the video, write a bunch of notes to summarize what I just
said.
And if any of this sounded not very familiar check out the description and you will find
a link to that full length lesson.
I am Mr. Tarrou.
BAM!
Go get that A, or that 5 like BAM!