Motion (9th Standard)
Motion
This post will help you understand the fundamentals of motion in a 1-dimensional as well as 2-dimensional surface.
Reference Point 🤔
Imagine you want to tell your friend your address. You take a certain landmark, and then give particular steps and directions for him to reach your home. As a result, anyone whom you would tell the same will arrive at your home every time.
Now imagine you're stranded in space with your spaceship. You have nothing around you. The rescue team asks you your location. Having no landmark nearby, you're unable to do so.
Now, if you were 200,000km away from Jupiter. You would tell the rescue team about the following taking Jupiter as a landmark.
From the above we can conclude that a landmark is required for you to locate an object. This landmark is called none other than the Reference Point.
Now we know that a reference point is required to locate an object. But what if the reference point is changed? What if the landmark of your address is a movable object which may change its location? The same steps you provided to your home will now no longer be able to guide the person to your desired location.
Therefore. the reference point is a fixed point considered in line-surface-space so that motion can be described easily by locating the position of the object.
Rest and Motion 👀
After learning about how we use a reference point to define the location of an object, now comes the topic of rest and motion. What are rest and motion? You must be familiar with these terms.
While sitting in a car with your father, according to your father you are at rest. But imagine your friend sees you pass by in the car. According to him you would be at motion. So how exactly can we say that an object is at rest or motion?
Observe how with different perspectives of your father and you friend, your state of rest and state of motion remains unclear. A major part of considering the state of rest or the state of motion of an object is perspective.
Rest can be defined as a state in which the position of an object does not change with time, with respect to the observer (perspective).
Motion can be defined as a state in which the position of an object changes with time, with respect to the observer (perspective).
Since you could be at rest as well as in motion with different perspectives, Rest & Motion are defined as relative terms.
Defining State of Rest or State of Motion of an Object:
An object is said to be at rest if its position with respect to its surroundings does not change with time.
Whereas, an object is said to be in motion if its position with respect to its surroundings changes with time.
Scalars and Vectors 🎯
Physical quantities are broadly classified into - (i) Scalar Quantities (ii) Vector Quantities
1) Scalar Quantities: Imagine you tell your friend the distance between your home (Point A) and his home (Point B) to be 8km. Here you indicate that there is a distance of 8km between yours and your friend's home. The direction of movement is undefined. These physical quantities are known as Scalar Quantities.
Scalar Quantities are the physical quantities expressed only by their magnitude. Example: Distance, Speed, Mass, Time, Temperature.
Scalar quantities follow the rules of fundamental arithmetic i.e. addition, subtraction, multiplication, division etc.
2) Vector Quantities: Imagine you draw a straight line between your home (Point A) and your friend's home (Point B) which turns out to be 5km. Here you indicate that you cover a distance of 5km between Point A and Point B (i.e. a straight line) in the direction of the straight line. Notice how #directionmatters.
Vector Quantities are physical quantities expressed by their magnitude as well as their direction. Their meaning is incomplete if either of them is missing. Example: Displacement, Velocity, Acceleration (All these terms are later explained in the blog).
Vector Quantities do not follow the fundamental rules of arithmetic. Instead they follow rules of vector algebra for their addition, subtraction, multiplication. (which will be discussed in higher classes).
Terms Related to Motion
Distance and Displacement 📏
1) Distance: The total length of path between two points is known as the distance of the path. Example: The length of path between Point A and Point B is 200km. So we can say that the distance of the path is 200km.
Distance can be defined as the total length of path through which a body moves. Distance is generally denoted by the letter D. It is always positive.
Since distance does not need a direction for its meaning to be complete, it is a scalar quantity.
2) Displacement: Imagine a straight line drawn on a paper between two points A and B. The length of this line is the length displaced by it or its displacement.
Displacement can be defined as the shortest line path from the initial position to the final position of a body. Its direction is always towards the final position. It is denoted by the letter S. It can be negative or positive depending upon its direction.
Since displacement is travelled towards the final position, its meaning is incomplete without specifying its direction. Hence displacement is a vector quantity.
Speed and Velocity 🚙
1) Speed
Ever noticed the dashboard of your car or bike? There's a speedometer which indicates the current speed of the vehicle. So what exactly is speed? Imagine you cover a distance of 2 meters in 1 second whilst running. This can also scientifically said that you cover a distance of 2 meters every second or 2 meters per second (written as 2m/s). This rate at which you cover distance is known as speed.
So, speed can be defined as the rate of change of body or the distance travelled by it per unit time. It is a scalar quantity since it does not represent the direction of the body. It is denoted by the letter S. Its SI unit is m/s or km/hr.
Uniform Speed or Uniform Motion: Suppose you cover a distance of 100m every 20 seconds. You are actually covering same distances in same intervals of time. Therefore, a body is said to be moving with a uniform speed if it covers equal distances in equal intervals of time throughout its motion.
Non-Uniform Speed or Non-Uniform Motion: Suppose you cover a distance of 1m every second as you start running, then your speed gradually increases such that you cover 5m every second, again eventually you get tired and cover 2m every seconds. Notice how you travel different distances and in the same intervals of time. Therefore, a body is said to be moving a non-uniform speed if it cover unequal distances in equal intervals of time. It is also known a variable speed.
Instantaneous Speed: As the name suggests, it is the speed of a body at a given instant. When the speed of a body keeps on changing, its speed at any instant is measured by finding the ratio of the distance travelled in a very short time to the time interval. This speed is called instantaneous speed. The speedometer of a car measures the instantaneous speed.
Instantaneous Speed = Distance travelled in a very short time / Time Interval
Average Speed: Suppose during your journey to a place, in the city you drive at a speed of 40km/hr, then on the highway you drive at a speed of 120km/hr, and while stuck in traffic jams you have a speed of 2km/hr. Now imagine you need to tell your speed during the journey to someone else. Would you tell all the details when your speed changed to the other person? No, right! Therefore an average speed during the journey is taken to give an estimate idea of speed.
The ratio of the total distance travelled by the body to the total time of journey is called its average speed.
In case of a body moving with uniform speed, the instantaneous speed and the average speed are same as the uniform speed since speed at any instant and all instants would be the same!
Average Speed = Total Distance Travelled / Total Time Taken
2) Velocity
Suppose you shoot an arrow, it travels certain distance in some time in a particular direction with a speed of 10m/s. This movement of the arrow in a particular direction per unit time is known as its velocity.
Hence, the velocity of a body is the distance travelled by it per unit time in a particular direction. OR we could say that the rate of change of displacement of a body with time is called its velocity.
Since velocity represents the magnitude as well as the speed of the body, it is a vector quantity. It is represented by the letter v or u. The SI Unit of velocity is the same as speed i.e. m/s.
Uniform Velocity: Uniform velocity is the same as uniform speed except that it's in a particular direction. Therefore, if a body travel equal distances in a particular direction in equal intervals of time it is said to be moving with a uniform velocity.
Example: (Rain drop example: explained later)
Non-Uniform Velocity: Non-Uniform Velocity is characterized by change in either the speed or the direction. Therefore, if a body travels unequal distances in a particular direction in equal intervals of time, or it moves equal distances in equal intervals of time but in different directions, it is said to be moving with a non-uniform velocity or variable velocity.
Example: The motion of a ball falling,
Instantaneous Velocity: For a body moving with variable velocity, the velocity of the body at an instant is called its instantaneous velocity. It's formula is the same as instantaneous speed. Though in the case of velocity, it is important to have time interval such that the direction of movement does not change during this period.
Average Velocity: It is the same as average speed. If the velocity of a body moving in a particular direction changes with time, the ratio of the total displacement travelled to the total time taken in its entire journey is its average velocity.
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