Summary
CBSE Class 9 || Physics || Motion || Animation || in English sreducators.com
IntroductionMotion is one of the key topics in physics. Everything in the universe moves, even if it's just a small amount of movement. In this lesson, we will learn about motion along a straight line, uniform and nonuniform motion, speed, velocity, acceleration, and the graphical representation of motion.
Understanding Motion
Motion is relative to the position of the observer. An object is considered to be in motion if its position changes with respect to an observer. For example, an automobile moving with respect to the ground is seen as motion by different observers. The Earth in its orbit around the sun is also considered to be in motion.
Motion Along a Straight Line
Everything in the world moves, even stationary objects such as a house. The motion can be purely vertical, horizontal, or slanted, but it must be along a straight line. When locating an object in physics, we usually relate it to a reference point, which is usually the origin. The position of an object is marked by its distance from the reference point, usually measured in meters.
Uniform Motion and Nonuniform Motion
In uniform motion, an object travels equal distances in equal intervals of time. In nonuniform motion, the object does not cover equal distances in equal intervals of time.
Speed
Speed is the rate of motion of an object and is measured by the distance traveled by the object in unit time. The SI unit of speed is meters per second (m/s). Average speed is used to describe the rate of motion of objects in nonuniform motion.
Velocity
Velocity is the speed of an object in a given direction. It describes both the speed and direction of the object's motion. Average velocity is calculated by finding the arithmetic mean of the initial velocity and final velocity of an object during a given period of time.
Acceleration
Acceleration is the rate of change of velocity with time. It describes the rate at which an object speeds up or slows down. Acceleration is measured in meters per second squared (m/s^2).
Graphical Representation of Motion
A graph is a pictorial representation of the relation between two sets of data. In a displacement-time graph, displacement is plotted on the y-axis and time is plotted on the x-axis. A straight line inclined with the x-axis represents uniform motion, while a curve represents nonuniform motion. The slope of a displacement-time graph gives the velocity of the object.
Conclusion
In this lesson, we learned about motion along a straight line, uniform and nonuniform motion, speed, velocity, acceleration, and the graphical representation of motion. Understanding these concepts is essential for studying physics.
It is not changing over time. This graph shows increasing speed. The moving object is accelerating. This graph shows decreasing speed. The moving object is decelerating.
This is a velocity-time graph of an object in nonuniformly accelerated motion.
Equations of Motion by Graphical Method The three equations of motion are:
v = u + at
s = ut + 1/2at^2
2as = v^2 - u^2
We use the initial velocity (u) of the object, which moves with uniform acceleration (a), for time (t). v is the final velocity and s is the distance traveled by the object in time t.
This equation describes the velocity-time relation. This equation represents the position-time relation. This represents the relation between the position and the velocity and can be obtained from these two equations. Let us go through them one by one:
Equation for Velocity-Time Relation
Consider an object moving with a uniform velocity (u) in a straight line. Let it be given a uniform acceleration (a) at time t = 0, when its initial velocity is u. As a result of the acceleration, its velocity increases to the final velocity (v) in time t, and s is the distance covered by the object in time t. The figure shows the velocity-time graph of the motion of the object. The slope of the vt graph gives the acceleration of the moving object. Thus, acceleration (a) is equal to slope, which equals BC/AC, which is equal to (v - u)/(t - 0), where a = (v - u)/(t). This equals v - u = at. V = u + at, which is the first equation of motion.
Equation for Position-Time Relation
Let the distance traveled by an object be s in time t and acceleration a. We can see that the distance traveled by the object is obtained by the area enclosed within. Therefore, distance traveled (s) is equal to the area of the trapezium ABDO, which equals the area of rectangle ACDO plus the area of triangle ABC, which is equal to OD x OA + 1/2 BC x AC. Now, putting the values, we get t x u + 1/2 (v - u) x t. On solving further, we get ut + 1/2 (v - u) x t. Now, from the first equation, we know that v - u = at, or we can write v = u + at. Therefore, s = ut + 1/2 at^2. This is the second equation of motion.
Equation for Position-Velocity Relation
The third equation will be obtained from these two equations. From the velocity-time graph, distance traveled (s) is equal to the area of the trapezium OABT. This is 1/2 (B1 + B2) x H, which is equal to 1/2 (OA + BD) x AC. Substituting OA by u, BD by v, and AC by t, we get s = 1/2 (u + v) x t. Equation 1. But we know that a = (v - u)/t, or t = (v - u)/a. Substituting the value of t in equation 1, we get v^2 - u^2 = 2as. 2as = (v + u) x (v - u). v + u x v - u = 2as. By using the identity a^2 - b^2 = (a + b) x (a - b), we can write v^2 - u^2 = 2as. This is the third equation of motion.
Uniform Circular Motion
Uniform circular motion describes the motion of a body traversing a circular path at a constant speed. The distance of the body from the axis of rotation remains constant at all times. As an object moves in a circle, it is constantly changing its direction. A merry-go-round is an example of uniform circular motion. Satellites orbiting our Earth (artificial satellites or our moon) have motions that are very nearly uniform circular motion. The planets that orbit our sun have motions that are very nearly uniform circular motion.
Did You Know?
Sir Isaac Newton is one of the most influential scientists of all time. He came up with numerous theories and contributed ideas to many different fields, including physics, mathematics, and philosophy. Born in England, Isaac Newton was a highly influential physicist, astronomer, mathematician, philosopher.