CLASS 9TH DAY 8
INTRODUCTION
MOTION
A body is said to be at rest if its position does not change with respect to its surroundings. Whereas, when the position of a body changes with respect to its surroundings, it is said to be in motion.
The state of rest and motion of the body is relative to each other. A body can be both at rest and in motion at the same time.
REST
If we look around us, we observe that many objects do not appear to move. Thus we consider them at the state of rest. Examples for the State of Rest:
- A book lying on the table will not change its position if it is not disturbed. So, it is in a state of rest.
- A bench in a park fixed under a tree is at rest as there is no change in its position.
Therefore, when the position of a body with respect to its surroundings does not change with time, the body is said to be at rest. A body is said to be at rest if its position does not change with respect to a fixed points in its surroundings.
MOTION
Unlike the above, we find that many things around us move from one place to another. A flying bird, a moving bus, a boy playing football, an oscillating pendulum of a wall clock, a moving train, a sailing ship, a walking man, etc. are some of the examples of motion.
A moving object keeps on changing its position continuously with time with respect to a fixed point called the reference point.
Examples for Motion:
- When a moving car changes its position with respect to a tree or a lamp post by the side of the road, the car is said to be in motion.
- A flying bird is also said to be in motion as it changes its position with respect to stationary objects such as trees.
Hence, when the position of a body with respect to its surrounding changes with time, the body is said to be in motion. One more example of rest and motion:
Suppose we are sitting on a railway platform and looking at a tree nearby. The tree is at rest because the tree does not change its position with respect to us. But when we see a train passing out of the station. The train is in motion because it is continuously changing its position with respect to us. A body is said to be in motion if its position continuously changes with respect to its surrounding changes with time.
REST AND MOTION ARE RELATIVE
A body can be both at rest and in motion at the same time. A body can be in motion relative to one set of objects while at rest relative to some other set of objects. Thus, rest and motion are relative. To understand this, consider the following examples.
Examples for relativity in rest and motion:
1. Suppose you are lying on your bed. You are at rest in relation to all other objects inside the bedroom. But the room (or home) is on earth and the earth itself is not at rest. The earth is revolving around the sun. It takes one year to complete one revolution around the sun. Thus, along with earth, you are also revolving around the sun. Hence in relation to the sun, you are in motion.
2. Next, consider a boy sitting on a bench in a park looking to a bus passing by on a road. For the boy, the bus is in motion but the trees in the park appear to be at rest. But to a boy sitting inside the bus, the trees and boy outside the bus will appear to move in the opposite direction and the roof of the bus or driver of the bus will appear to be at rest.
3. If two trains move at the same speed and in the same direction on two parallel railways then both trains will appears stationary to the passengers sitting in them.
Thus, we conclude that a body while in motion with respect to a set of objects can appear at the same time in a state of rest with respect to some other set of objects (moving at the same speed and in the same direction). It is an observer and the surroundings that decide whether a given object is at rest or in motion.
Scalar and Vector Quantities
There are a lot of different mathematical quantities used in physics. Examples of these include acceleration, velocity, speed, force, work, and power. These different quantities are often described as being either “scalar” or “vector” quantities. Below we will discuss what these words mean as well as introduce some basic vector math.
What is a scalar?
A scalar is a quantity that is fully described by a magnitude only. It is described by just a single number. Some examples of scalar quantities include speed, volume, mass, temperature, power, energy, and time.
What is a vector?
A vector is a quantity that has both a magnitude and a direction. Vector quantities are important in the study of motion. Some examples of vector quantities include force, velocity, acceleration, displacement, and momentum.
What is the difference between a scalar and vector?
A vector quantity has a direction and a magnitude, while a scalar has only a magnitude. You can tell if a quantity is a vector by whether or not it has a direction associated with it.
Example:
Speed is a scalar quantity, but velocity is a vector that specifies both a direction as well as a magnitude. The speed is the magnitude of the velocity. A car has a velocity of 40 mph east. It has a speed of 40 mph. Click below to learn more about scalar and vector quantities.👇 👇
Distance and Displacement
I’ve got to assume that everybody reading this has an idea of what distance is. It’s one of those innate concepts that doesn’t seem to require explanation. Nevertheless I’ve come up with a preliminary definition that I think is rather good. Distance is a measure of the interval between two locations. (This is not the final definition.) The “distance” is the answer to the question, “How far is it from this to that or between this and that?”
For example, Delhi is 1415 km away from Mumbai. You get the idea. The odd thing is that sometimes we state distances as times.
How far is it | Possible answer | Standard answer |
90 minutes per orbit | 40,000,000 m | |
90 minutes by train | 00,150,000 m | |
90 minutes on foot | 00,010,000 m |
They’re all ninety minutes, but nobody would say they were all the same distance. What’s being described in these examples is not distance, but time. In casual conversation, it’s often all right to state distances this way, but in most of physics this is unacceptable.
That being said, let me deconstruct the definition of distance I just gave you. Every year in class, I do the same moronic demonstration where I start at one side of the lecture table and walk to the other side and then ask “How far have I gone?” Look at the diagram below and then answer the question.
There are two ways to answer this question. On the one hand, there’s the sum of the smaller motions that I made: two meters east, two meters south, two meters west; resulting in a total walk of six meters. On the other hand, the end point of my walk is two meters to the south of my starting point. So which answer is correct? Well, both. The question is ambiguous and depends on whether the questioner meant to ask for the distance or displacement.
Let’s clarify by defining each of these words more precisely. Distance is a scalar measure of the interval between two locations measured along the actual path connecting them. Displacement is a vector measure of the interval between two locations measured along the shortest path connecting them.
How far does the Earth travel in one year? In terms of distance, quite far (the circumference of the Earth’s orbit is nearly one trillion meters), but in terms of displacement, not far at all (in some respects, zero). At the end of a year’s time the Earth is right back where it started from. It hasn’t gone anywhere.
The above figure shows a trip to New Jersey. Getting there is a three step process.
- Follow the Hudson River 8.2 km upriver.
- Cross using the George Washington Bridge (1.8 km between anchorages).
- Reverse direction and head downriver for 4.5 km.
The distance traveled is a reasonable 14 km, but the resultant displacement is a mere 2.7 km north. The end of this journey is actually visible from the start. Distance and displacement are different quantities, but they are related. If you take the first example of the walk around the desk, it should be apparent that sometimes the distance is the same as the magnitude of the displacement. This is the case for any of the one meter segments but is not always the case for groups of segments. As I trace my steps completely around the desk the distance and displacement of my journey soon begin to diverge. The distance traveled increases uniformly, but the displacement fluctuates a bit and then returns to zero.
The SI unit of distance and displacement is the meter [m]. To learn more about distance and displacement, Click on the link below👇 👇
Speed and Velocity
Speed
What’s the difference between two identical objects traveling at different speeds? Nearly everyone knows that the one moving faster (the one with the greater speed) will go farther than the one moving slower in the same amount of time. Either that or they’ll tell you that the one moving faster will get where it’s going sooner than the slower one. Whatever speed is, it involves both distance and time. “Faster” means either “farther” (greater distance) or “sooner” (less time).
Doubling one’s speed would mean doubling one’s distance traveled in a given amount of time. Doubling one’s speed would also mean halving the time required to travel a given distance. If you know a little about mathematics, these statements are meaningful and useful. (The symbol v is used for speed because of the association between speed and velocity, which will be discussed shortly.)
- Speed is directly proportional to distance when time is constant: v ∝ s (t constant)
- Speed is inversely proportional to time when distance is constant: v ∝ 1t (s constant)
Combining these two rules together gives the definition of speed in symbolic form.
v=s/t
This is not the final definition. Don’t like symbols? Well then, here’s another way to define speed. Speed is the rate of change of distance with time.
In order to calculate the speed of an object we must know how far it’s gone and how long it took to get there. “Farther” and “sooner” correspond to “faster”. Let’s say you drove a car from New York to Boston. The distance by road is roughly 300 km (200 miles). If the trip takes four hours, what was your speed? Applying the formula above gives…
v=s/t = 300km/4hour = 75km/hr
ΔThis is the answer the equation gives us, but how right is it? Was 75 kph the speed of the car? Yes, of course it was… Well, maybe, I guess… No, it couldn’t have been the speed. Unless you live in a world where cars have some kind of exceptional cruise control and traffic flows in some ideal manner, your speed during this hypothetical journey must certainly have varied. Thus, the number calculated above is not the speed of the car, it’s the average speed for the entire journey. In order to emphasize this point, the equation is sometimes modified as follows…
v=ΔS/ΔT
The bar over the v indicates an average or a mean and the ∆ (delta) symbol indicates a change. Read it as “vee bar is delta vee over delta tee”. This is the quantity we calculated for our hypothetical trip.
In contrast, a car’s speedometer shows its instantaneous speed, that is, the speed determined over a very small interval of time — an instant. Ideally this interval should be as close to zero as possible, but in reality we are limited by the sensitivity of our measuring devices. Mentally, however, it is possible imagine calculating average speed over ever smaller time intervals until we have effectively calculated instantaneous speed. To learn more about speed, click below👇 👇
Velocity:
In order to calculate the speed of an object we need to know how far it’s gone and how long it took to get there. A wise person would then ask, Would do mean by how far. Do you want distance or displacement ?
Your choice of answer to this question determines what you calculate — speed or velocity.
- Average speed is the rate of change of distance with time.
- Average velocity is the rate of change of displacement with time.
Speed and velocity are related in much the same way that distance and displacement are related. Speed is a scalar and velocity is a vector. Speed gets the symbol v (italic) and velocity gets the symbol v (boldface). Average values get a bar over the symbol. Velocity (v) is equal to displacement (d) divided by time (t).
Displacement is measured along the shortest path between two points and its magnitude is always less than or equal to the distance. The magnitude of displacement approaches distance as distance approaches zero. That is, distance and displacement are effectively the same (have the same magnitude) when the interval examined is “small”. Since speed is based on distance and velocity is based on displacement, these two quantities are effectively the same (have the same magnitude) when the time interval is “small” or, the magnitude of an object’s average velocity approaches its average speed as the time interval approaches zero.
Δt—–>0 => v—->|v|
The instantaneous speed of an object is then the magnitude of its instantaneous velocity.
v = |v|
Speed tells you how fast. Velocity tells you how fast and in what direction. To learn more about velocity click below👇 👇
Units:
Speed and velocity are both measured using the same units. The SI unit of distance and displacement is the meter. The SI unit of time is the second. The SI unit of speed and velocity is the ratio of two — the meter per second.
This unit is only rarely used outside scientific and academic circles. Most people on this planet measure speeds in kilometer per hour (km/h or kph). Take the quiz below to test you knowledge👇 👇
Now I am sure you have a pretty good idea. Now let’s take a quiz to check our understanding .
Kakuro
The game of Kakuro is also called Cross Sum puzzle. Look at the game rules.
About the game: The Kakuro puzzle is of different size of length and width, although most puzzles are squares. The Kakuro has 3 different boxes.
- A clue box – which has usually a number on the bottom and/ or on the right side.
- A white blank box – that is where you fill in the a number between 1 and 9.
- A block box – that is the black box.
Rule : Place one digit from 1 to 9 in each empty box so that the sum of the digits in each set of consecutive white boxes(horizontal or vertical) is the number appearing to the left of a set or above the set. No number may appear more than once in any consecutive boxes.
How to solve: We take here a easy example:
Step 1: There are 2 clues for the A box, 7 for the top and 6 for the left.
We know that to get a 6 with the combination of 4+2 and 5+1. Meaning the number 1,2,4 , or 5 will be in box A.
Step 2: We look now to the left, box B. There we have the clues on top 3, and left 6. We know that to get a 3 the only combination that can be is 1+2.
Step 3: In box D, there the clue 3 to the top and clue 4 to the left. We know that 3 is 2+1. And that 4 is 3+1. So the number 1,2, or 3 can be in box D.
Step 4: In box C, we have the 4 to the left and 7 on top. The combination for 4 is, 3 +1 .
Here we can conclude that in D 2 is eliminated from the possible solutions because in to make a 4 there is no 2.
Looking to the top of C, a 7. the combinations of 1+6, 2+5, 3,+4. Now 1+6 is not a possibility because A can not hold a 6, step 1. Also 2+5 is not an answers, because in D can only be 3 or a 1. As a consequence 3 is the only possible solution for C. as a consequence D is 1, and B is 2. The only possibility for A is 4. To learn more about Kakuro, Click below👇 👇
JIVAN GYAN
Today we will learn about 5-6 Yoga poses which will help boost your memory. Practice these daily and that will help you brush up your memory power and it also gives power to your brain. Click on learn more to watch the video explaining the same.
