Good morning. The position of an object is described by the equation position equals 2.5
times time in the i direction plus the quantity 2.5 times time minus 4.9 times time squared all
in the j direction all in meters. Bobby, please determine the velocity and Bo, please determine
the acceleration, of this object. ♪ Flipping Physics ♪
Uh, velocity is the derivative of position with respect to time. So,
velocity equals the derivative of that equation with respect to time.
That equals 2.5 i plus the quantity 2.5 minus 2 times 4.9 or 9.8 t all times j
all in meters per second. And acceleration is the second
derivative of position with respect to time or the derivative of velocity with respect to time. So,
acceleration equals the derivative of the velocity equation Bobby just found. Or well, the derivative
of both constants equals zero, so it just ends up being negative 9.8 j meters per second squared.
Great. Now we have the position, velocity, and acceleration of the object as a function of
time in both the i or x-direction and j or y-direction. That means we can now determine
the object’s position, velocity, and acceleration at any time t. All we have to do is substitute
that time t into each equation. Does anyone notice anything special about this motion?
It’s uniformly accelerated motion. Right, acceleration of the object
does not change as a function of time because this object is in uniformly accelerated motion.
Its acceleration is constant. Actually, we should have known that at the very beginning.
Yeah, the highest exponent in the position vector is 2.
Billy. Right, and if the highest exponent in the position vector is 2 or less,
the object is in uniformly accelerated motion. It’s difficult to remember everything.
It is difficult. That is why we practice. You should not expect yourself to remember
everything after learning it once. Okay, let’s identify what we can see when I rearrange the
position vector like this. I have added a zero at the beginning and combined all
the terms with time to the first power and the only term with time to the second power
is at the end. Does this look familiar to anyone? Not really. Uh. I do not know.
We already identified this as uniformly accelerated motion.
Oh, it is one of the UAM equations. Really?
Yeah. Which one? R position equals r position
naught plus velocity naught times time plus one-half times acceleration times time squared.
Wow, it really is. Then we know the initial position equals zero.
And the initial velocity equals 2.5 i plus 2.5 j meters per second.
And we can determine the acceleration to be negative 9.8 j meters per second squared,
just from the r position vector. Cool. Actually, this is an equation for an object in
projectile motion. It has an acceleration in the j or y-direction of -9.8 meters per second squared
and a constant velocity in the i or x-direction of 2.5 meters per second. Yeah,
it’s projectile motion. How do you know that?
Uh, I have not learned about projectile motion yet.
I watched some of the videos for next week already.
What? Really? Why?
Bored. Pandemic. Ah, yeah. Coronavirus.
Very nice y’all. We can glean a lot of information from the r position vector when
we recognize it to be one of the uniformly accelerated motion equations. And yes, Bo,
this does represent an object in projectile motion. If you do not understand that yet,
do not worry, projectile motion is what we are learning about next.
Thank you very much for learning with me today, I enjoyed learning with you.
Should we be wearing masks? If we were in the same room together,
yes. Uh, what?