Linear Motion and Kinectics

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[Video begins] [Scene displays a Power Point presentation] [This document contains only the audio portion of this presentation] [Ciocca] Welcome to our second video lecture. This video lecture is about chapter three, in particular linear motion. If you notice we are going to chapter three first then we are going to go back to chapter two. The reason being that in chapter three we can introduce some quantities that will be useful to understand chapter two better. So, without any further ado, this is chapter three linear motion.

As the name suggests, this is the motion that occurs when the movement is in a straight line. There will be no curves to it, just a straight line motion whether it is up and down, left to right, doesn’t matter. But, in this case the motion will be straight. In order to understand the quantities that will come later, the first quantity that we are going to introduce is the quantity called speed. You are probably familiar with it, but you have to remember that quite often in physics we use terms that you think you know but in physics they are very precise and perhaps a different meaning from the one you know. In this case this is not the case, but we will encounter some.

Anyway, speed is defined as the distance covered per amount of travel time. So, notice that the quantity is distance divided by time. Now, in physics and the sciences in general quantities have units. So, in this particular case, distance in physics is measured using the quantity known as meter. And, time is measured in seconds. That’s pretty common. Meters are not as common as the second is. Second is used everywhere, the world over. Meters in used in science mostly and in Europe. In the United States they use feet, yard, inches. In the sciences however, we are going to limit ourselves to using the meter. So, in equation form the speed is defined as distance divided by time, and in unit as meters per second. As an example, example one, this girl runs 4 meters in 2 seconds. Notice that there is no direction involved here so we are assuming that she is moving in a straight line. And, her speed will be 2 meters per second. Sometimes it will be useful to define a quantity called average speed. Notice the term average indicates that this is not the speed instant by instant, but more like the speed that this object moving has over the entire motion. Here the total distance—notice the word total—is divided by the total travel time. So, it is still distance over time, but this time we don’t pay attention to the details of the motion. We look at the entire movement divided by the entire time as to indicate the various instantaneous speed along the way. For example, when you come to school from home you enter the car and you start the engine. Your speed at that time is zero, you haven’t moved much. However, you start moving, drive towards school, you have a red light, you stop. You were moving at a certain speed and then when you stop you’re moving at another.

To kind of give an idea of the total motion, we introduce average speed as the total distance covered divided by the time interval. It still has the units of meters per second, but has a different meaning. For example, you drive a distance of 20 kilometers in 2 hours. Well, your average speed is clearly two hundred divided by 2 hours, or 100 kilometers per hour. You may have gone faster sometimes than 100 kilometers per hour, sometimes slower, but your average is one hundred. It’s useful though to still have the idea of instantaneous speed. Instantaneous speed is the speed at any instant at a particular time. For example, when you ride in your car you might speed up or slow down. Your odometer will tell you that at that instance in time you are doing a hundred and then a few minutes later will be doing at ninety, and then another time later 120 kilometers per hours, kilometers per hours, and so on and so forth. You are doing that speed at that instance in time, not all the time. Instantaneous speed therefore can be viewed as the one given by your speedometer in the car. This is somewhat new.

Now, we are going to introduce velocity. Velocity is the description of both the instantaneous speed of the object and the direction of travel. So, now we are going to specify not only how fast, which is given by the instantaneous speed, but also which way. In other words, we are introducing a quantity that is called vector. It’s a quantity that has a magnitude indicating how long—how big is the vector and a direction which indicates which way the particular vector is going. So, velocity is a vector quantity. It has magnitude, which in this case will be the speed, and a direction. So, velocity can be seen as directed speed. Here’s some more definitions. Constant speed, as the name suggests, is a speed that doesn’t change. The object is not speeding up nor is it slowing down. Constant velocity on the other hand is something that is a bit more strict. Not only the speed is constant, but also it’s a constant direction. That is, it’s a straight line path with no acceleration. The velocity that is constant means that the speed is fixed and the direction is fixed. All these quantities, speed and velocity, that we have introduced are all relative Earth unless specified otherwise.

Now, we are going to introduce the idea of acceleration. Acceleration was formulated by Galileo based on his experiments with inclined planes and it is the rate at which the velocity changes over time. Let’s write it down in equation format. You will see that on the next slide. For example, imagine the following. If you have a ball rolling down an inclined plane, like in this case here, the slope is downwards so the speed of the ball rolling down will become bigger and bigger. This is called positive acceleration. In the slope upward the motion is in the direction of the arrow, as you can see, but the speed is decreasing. That is, the speed is getting smaller. That implies that the acceleration in this case is in the opposite direction. That is, it is this way. In this case, the acceleration on the other end is that way. Notice that these two arrows are pointed in the same direction, these are opposite, so we can conclude in this case you can say that the acceleration is opposing to the speed. Therefore, this can be viewed as negative acceleration. If no slope and the ball is rolling at a constant speed, a speed that has no change, then this constant velocity. Be careful. When we talked about acceleration this involves either a change in speed or a change in direction or both.

So, for example if you have a car making a turn or a car going around a track and it is moving at the same constant speed, but notice that the trajectory is a circle. This implies that the velocity is changing even though the speed may not.

An example again, imagine you have a car that goes around a track like this. Your speedometer will be saying 100 kilometers per hour all the time as you go around the track in your car. Your speed is constant, but the velocity is not. Because, look. Here, this is the velocity V. As you go around the track when you are up here the velocity is this way. When you are here, the velocity is that way. When you’re here, the velocity is this way. You see it’s changing continuously. Therefore, in this case the speed is constant but the velocity is not. Therefore, you do have acceleration.

We are ready to give a definition of velocity in terms of an equation. The acceleration is defined as the change in velocity divided by the time interval. Notice the velocity and speed are of the same units. They are still meters per seconds and the time interval are still seconds. So, this quantity here, the acceleration, has the units of meters per second per second, or meters per second squared. So, if your car speed is say 40 kilometers per hour and 5 seconds later it is forty-five. The car change in speed is forty-five, 5 kilometers per hour, and your car acceleration is 1 kilometers per hour per second which is a very strange unit. We’ll try to use the units of time which are common for the two, was able to study the idea of acceleration by observing the motion of a ball down an inclined plane at large and larger angles. When incline is vertical the acceleration is maximum, the same of that of a falling object. When air resistance is negligible, all objects fall with the same unchanging acceleration. And, Galileo was able to show that the acceleration in this case of an object falling, a, is approximately 10 meters per second squared. In general, the more precise value of the acceleration in this case for freefall is given its own name because it is so constant. It is called g and is equal to 9.8 meters per second squared. As you can see, this is true only when there is no air resistance. So, this is called free fall. A free falling object on Earth accelerates at the rate of approximately 10 meters per second per second, or 10 meters per second squared. And, like I said before, more precisely 9.8 meters per second squared. I apologize for those big two’s, it should be seconds squared. …as an acceleration which is constant. What does it means in terms of velocity? It means that the velocity changes by the same amount every second. So, in this particular case, the velocity which is acceleration times time is given this way. Notice that you have an object falling and the free fall when acceleration is 10 meters per second it means that speed is 10 meters per second after 1 second, ten more after 2 seconds gives you twenty, ten more after 3 seconds gives you thirty, and so on. [Video ends]