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2. 1D Motion / Kinematics

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Hey, guys. So in this video, we're gonna talk about acceleration, which is a variable that's useful. Not just emotion problems, but for the rest of physics. So it's really important you learn stuff very well. And what we're gonna see is the acceleration actually has a pretty simple formula. So let's check it out. So you guys remember what we talked about? Velocity velocity was a measure of how fast your position changed. The equation was V equals Delta X over Delta T your displacement over time. Well, in a very similar way, the acceleration is a measure of how fast your velocity changes. So let me recap again. Velocity is measured. How how fast your position changes acceleration, how fast your velocity changes. The equation is very similar. The letter will use for acceleration is a instead of Delta X over tea. It's Delta V over Delta t the units for this, they're gonna be in meters per second squared. So anytime you see those units, we're always gonna be talking about acceleration. So this equation actually tells us that there's two ways that something can have acceleration or can accelerate. It's either the object changes the velocities magnitude. So either is the change in the velocities magnitude or a change in the direction. Because remember that the velocity is a vector and it has both magnitude and direction. So if either one of these things changes, that means that the vector changes and that means that there is some acceleration. So let's actually talk about that. The acceleration is a vector because it depends on a vector. What's different about the acceleration is that it's always a vector, and what I mean by that is that there's no scaler version of the acceleration. So let's recap all the variables that we know so far. When we studied displacement, murder, displacement had a scaler equivalent that was a distance that was on Lee Magnitude, not direction. And then from the displacement we got the velocity. The velocity was magnitude and direction, but it had a scaler equivalent, which was speed. That was just the number, no direction. Well, from the velocity, we can actually get the acceleration. And what's different about this is that there is no scaler equivalent for the acceleration, So acceleration is just always a vector, and it always has magnitude and direction. Alright, guys, so that's really all you need, others to it. It's a simple equation, so let's just get to some examples. So we've got a car moving to the right and 10 m per second, and then after some time, we're moving to the right of 30. So let's just draw this out. So we know that velocities are vectors with magnitudes and directions, so I'm gonna draw this out. My initial velocity is 10 and we're saying that we're going to the right. So it's some later time. Now we have a different velocity. So basically this number here is 30 m per second is higher and we're also moving to the right, so it's a little bit longer and RV is 30 m per second. And we know that the time that it took to do this my delta T was four seconds. So now we want the magnitude and the direction of the acceleration. So let's just go through our formula. We know that we want A and we know that a is just the Delta V over Delta t change in velocity of change in time. Well, whenever we did Delta X, we kind of used the X final minus X initially expanded that term out It works the same way here by changing velocity is just my final velocity minus initial velocity over Delta T. So my final velocity is 30. My initial velocity is 10 and my delta T is four. So I just get 20/4 and I get 5 m per second squared. So that's my answer. 5 m per second. That kind of looks like a nine. So let me just read that. Here we go. So we got 5 m per second squared, so we know that the acceleration equals five. But what about the direction? We'll notice how we got a positive number here because we plugged into positive numbers and we chose the right direction to be positive because that was basically the number that was increasing this direction. So that means that acceleration vector points this way. Let's move on to the second one. We're talking to the right at 6 m per second three seconds later, were drawn into the left, 6 m per second. So let's draw that out. So we've got initial velocity. My V knots is gonna be six in this direction and then at some later time now we have a velocity and we're jogging to the left at 6 m per seconds. That means that my final velocity looks like this. It's the same length of the arrow. It's just backwards. So this final velocity is six. We have to be careful here because we chose this direction to be positive. That's normally what we dio in problems, which means that this direction is negative. So we have a velocity that points to the left, which means that it picks up a negative sign. So it's negative six. So even though problems don't tell you that's negative, you're gonna have to sometimes infer it from the text or figure it out. So what's the magnitude and the direction of the accelerations? We're just gonna use the same exact formula. We also know that the time that it takes for this to happen, this Delta T is equal to three seconds. So my acceleration, we're just gonna use my Delta T or Delta V over Delta T. So now what's the the final minus of the initial? Well, it might be final is gonna be negative. Six. My the initial is gonna be positive. Six and my adult cities three. So we've got negative six minus positive six, which is negative. 12/3, and I get negative 4 m per second squared. So now that's the magnitude. That magnitude is four now. What about the direction? So we know that a is equal to four. What about the direction? Well, again, the negative sign usually tells us the direction in physics. So because we got something that points or that has a negative sign, then that means that the acceleration vector actually points to the left. So that is the direction. So I kinda wanted to point out again because I made this point earlier that there's two ways that something could have acceleration. Either you change the velocities magnitude. In this case, we went from 10 to 30 or you can change the direction. In this case, we went from positive six to the rights and then negative six to the left. So it's the same number. The only thing that changed was the direction, and that's because there's a sign. Change eso anyway, So that's it for this one. Let me know if you have any question

2

Problem

The brakes of your car can provide an acceleration of 4.6m/s^{2}. You’re speeding at 37.5 m/s and suddenly see a police car, so you slam the brakes. How long will it take for your car to slow down to the speed limit of 25 m/s?

A

0.37 s

B

33 s

C

2.7 s

Additional resources for Intro to Acceleration

PRACTICE PROBLEMS AND ACTIVITIES (7)

- A car sits on an entrance ramp to a freeway, waiting for a break in the traffic. Then the driver accelerates w...
- A car sits on an entrance ramp to a freeway, waiting for a break in the traffic. Then the driver accelerates w...
- A rocket starts from rest and moves upward from the surface of the earth. For the first 10.0 s of its motion, ...
- A rocket starts from rest and moves upward from the surface of the earth. For the first 10.0 s of its motion, ...
- A turtle crawls along a straight line, which we will call the x-axis with the positive direction to the right....
- CALC. A car’s velocity as a function of time is given by v_x(t) = α + βt^2, where α = 3.00 m/s and β = 0.100 m...
- A race car starts from rest and travels east along a straight and level track. For the first 5.0 s of the car’...

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