Unit+6

Motion - Unit 6 Motion is all around us. One of the earliest goals of scientists was to explain motion. In this chapter, you will learn to describe simple forms of motion. You will also learn some causes of this motion. =Position= How do you know where you are? Right now you are sitting in front of a computer in your classroom. But, where is

your classroom? The word science uses to describe something's location is position. Position is just another way of saying where something is.

Position is relative. This means that position is "related" to some other position. Another way to look at it is that position is defined by some reference point. You could say that the position of your desk is in the third row from the front of the class. In this case, your reference point is the front of the class.

Once a reference point is chosen, reference directions are needed. We usually use north, west, south, and east as reference directions. North is the direction to the north pole, south is the opposite direction, and east and west are perpendicular to north-south. Other reference directions include up and down. To describe one's position, one needs to have a reference point or position and directions from that point.

=Speed= In your mind right now, the idea for SPEED might just be "fast" and "slow". We use descriptions like "this train is slower then that train, therefore, this train takes us from here to there slower". These words are used to compare speed, but they are not precise enough. We need to define speed carefully.



Imagine, a man driving a car steadily. When he passed a traffic light, we start timing it and record the progress each second. It is shown on the picture above. The driver is going at a steady speed. We define speed as the distance traveled each given time unit, such as a second. This driver is going 10 meters per second.

WORKING WITH SPEED

Trying to find the speed might not be as hard as you think. It's fairly simple, you will only need two numbers. The time that it was taken, and the distance it has traveled. After you've got those two number, calculating speed is a cinch. You can then just divided distance by time to get the speed.

Average Speed It's like the average of your grade. You might have an A and a C, but your average is a B. Science works a lot like mathematics, you add all the numbers together, then divide by how many numbers you've added. For example, if a car is traveling 50 meters per hour, but was slowed down to 10 meters per hour while crossing the school zone.
 * **Speed =** || **__Distance__** ||
 * ^  || **Time** ||

In this case, the car is not going at a steady speed. The speed changes continually, therefore, AVERAGE SPEED is being used. We can use the formula **speed = total distance / total time** Their average speed is 30 meters per hour. (50 + 10 = 60, 60/2 = 30) Next, let's contrast average speed to **instantaneous speed**. Well, as you might have guessed, instantaneous speed is the speed at which you are currently traveling at the moment. For instance, if you are driving along and look down at the speedometer, your instantaneous speed at that moment would be what was displayed on your speedometer. So, how does instantaneous speed differ from average speed? Well, let's go back to the example above. One way to get an average speed of 50 mph over 2 hours would be to simply drive at 50 mph all the time. In this case, the average speed would be the same as the instantaneous speed. However, let's say your foot is not the steadiest part of your body. If this is true, then your instantaneous speed would fluctuate a lot. However, if you still manage to cover 100 miles in 2 hours, even though your speed was fluctuating, then your average speed would still be 50 mph, but your instantaneous speed during those two hours of driving would not always be 50 mph.

Distance Time Graphs
Distance-time graphs is a way to visually show a collection of data. It allows us to understand the relationships between the data. The below is a example of a distance time graph. Distance(m) Time (s) ||  ||   ||
 * Distance-Time for Table 1
 * Distance (s) || Time (s) ||
 * 0 || 0 ||
 * 1 || 13 ||
 * 2 || 25 ||
 * 3 || 40 ||
 * 4 || 51 ||
 * 5 || 66 ||
 * 6 || 78 ||


 * As you can see, the data from the table is shown in a visual format in the graph. The time (s) is shown as the x axis and the distance (m) is shown on the y axis on the graph. The points on the graph do not create a perfectly straight line so a //line of best fit// must be drawn //in.// ||

=Velocity=
 * Velocity** is just like speed, except you add a direction to it. For instance, for speed, you would say," This car is going 55 meters per hour." But if you where talking about velocity, you would add the direction of which the car is going. For example, " This car is going 55 meters per hour, north."

=Acceleration= If you are blind-folded sitting in a smooth driving quiet car. You won't be able to tell if you are traveling, unless the car speeds up, slows down, or changing direction. A change of velocity, or you can also think of a change in speed or direction of an object, is called **acceleration**. When an object gets faster, it accelerates.

Acceleration = final velocity - initial velocity / time
 * Acceleration** - the rate of change in velocity. If something is accelerating, its velocity is changing over time. You can use that definition to determine the equation needed to find an object's acceleration.

Acceleration tells you haw fast velocity is changing over time. What units are used to express acceleration? Well, if velocity is measured in km/h and time is measured in hours then the acceleration unit is km/h/h or km/h2. This means that if an object is acceleration at 50 km/h2, each hour its velocity increases by 50km/h. Example problem A roller coaster's velocity at the top of a hill is 10 m/s. 2 seconds later, it reaches the bottom of the hill with a velocity of 26 m/s. What is the acceleration of the roller coaster? Initial velocity = 10 m/s Final velocity = 26 m/s Time = 2 s Acceleration = final velocity - initial velocity / time __=16 m/s__ || = = = 8 m/s/s || The unit for acceleration is fairly strange. It is in this case, meter per second per second. 2 meters per second per second seems strange, but when you really think about it, it would become more clear. It increases certain "speed" per second. Since the unit for speed is meters per second, therefore, "meters per second" per second would be a correct way of saying it increases certain speed every certain time interval.In the picture below, the car is shown for each second. The speed of the car is also shown. The car's speed is increasing steadily. It is called c**onstant acceleration**.
 * A = || __26 m/s - 10 m/s__ || = =
 * || 2s || 2s ||  ||

In this case, the car accelerates at 2 meters per second (how fast the care is moving in one second). And the correct way to say it is 2 meters per second per second or 2 meters per second squared. Objects that are slowing down are said to have negative acceleration or **deceleration**. The same equation is used to find an object's deceleration. Example problem At the end of a race, a bicycle is decelerated from a velocity of 12 m/s to a rest position in 30 s. what is the average deceleration of this bicycle? Final velocity = 0 m/s Initial velocity = 12 m/s Time = 30 s A= v /t A = __0 m/s - 12 m/s__ == __- 12m/s__ = - 0.4 m/s/s 30 s 30 s

CIRCULAR MOTION With the subject of motion in more than one dimension broached, we can consider things other than simple linear motion. For example, many types of motion involve curved paths rather than linear ones. We have already seen one example in the parabolic shape of the trajectory of an object in free-fall. Another example is simply the motion of an object in a circular path. This includes motions as diverse as cars on a Ferris wheel to satellites in orbit around the earth. This kind of motion is somewhat special in that the object of interest maintains a constant speed as it goes around the circle (i.e. the magnitude of its velocity doesn't change.) However, the direction of the velocity does have to change continuously to maintain the circular path. Whenever the velocity magnitude, direction, or both is changed, there must be a non-zero acceleration acting to change the motion.

An object that is in uniform circulation, will have a constant speed. For example, if a car is going around a circular track, at a uniformed rate of 90 km/h (55m/h) had a constant speed. However, the velocity (speed + direction) of the car will not be constant, because the velocity in continually changing direction. Since there is a change in velocity, there is an acceleration.