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Motion in one dimension

We live in a 3-dimensional world, so you might be thinking why should we bother analyzing 1-dimensional situations? Basically, because in any translational motion that is straight-line motion problem can be separated into one or more 1-dimensional problems that is a complex problem in physics can be analyzed by reducing it into a series of simpler problems. So to solve a problem you have to first set up a coordinate system which defines an origin or a starting point and positive and negative directions as well. And also you need to differentiate between scalars and vectors. Motion in one dimension is one of the earliest lessons found in Newton’s Classical Mechanics. Whenever a body moves with respect to time and its surroundings, the change in position of the body is known as motion. For analyzing the motion of objects in one dimension there are four basic parameters you need to be aware of. These four basic parameters are namely displacement, velocity, and acceleration and time. Among these four time is a scalar quantity, while the other three are vectors quantity. However, in 1 dimension, it's quite differentiate between a scalar and a vector and that difference will be more clear in 2 dimensions.

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Displacement

The displacement represents the distance traveled in certain direction which signifies that it is a vector quantity. Displacement(∆x) is defined as the difference between your final position denoted by x and your starting point denoted by xo. So in 1-dimension displacement ∆x=x- xo

Speed and Velocity

Average speed is defined as the ratio of distance covered to elapsed time.ven by = distance covered / elapsed time
On the other hand, the average velocity defined as the ratio of displacement to the elapsed time.
So average velocity is given by = displacement / elapsed time.
Average velocity can be zero as displacement can be zero but average speed can never be zero as distance covered is always a positive and finite quantity.
The instantaneous velocity v is defiThe instantaneous velocity v is defined as the rate of change of position of a moving particle with time, for a very small time interval. If we consider the displacement to be ∆x and the time interval be ∆t, then the instantaneous velocity during that time interval is given by: ∆x/∆t
And the instantaneous speed is simply the magnitude of the instantaneous velocity as speed is a scalar quantity whereas velocity is a vector quantity.

Acceleration

An object accelerates means its velocity changes which can be either positive acceleration or negative acceleration known as deceleration..Similar to the average velocity, the average acceleration is defined as the ratio of change in velocity over a very short time interval.
The instantaneous acceleration is given by: acceleration, a=∆v/∆t. As velocity is vector quantity and acceleration is defined by the change in velocity over an interval of time, so acceleration is also a vector quantity

Kinematics and Dynamics

Kinematics is concerned with the part of mechanism which deals with motion of an object and its descriptive knowledge without considering the reason of origin.

Whereas dynamics is concerned with the study of motion of an object related to its cause.

Motion in One Dimension

Motion of an object in a straight line is called motion in one dimension. The position of an object or particle is described only by one variable which is indicated either by x. For a moving particle along with a straight line (1-D), all vector quantities such as velocity, position, displacement and acceleration have only one non zero component.

Motion in Two Dimensions

Motion in two dimensions is concerned with motion of a particle and an object in a plane. For two dimension motion velocity and acceleration can be described by 2 components in two mutually perpendicular directions in Cartesian coordinate system. Thus vector quantities such as velocity, displacement, position and acceleration have two non-zero components.

Equations of Motion with constant acceleration

a.   v = u + at
b.   S = ut + 1/2(at²)
c.   v² = u²+2as

Where u = initial velocity, v= final velocity, s = displacement

Displacement in n^th second

S_n=u+a/2(2n-1)

Equation of motion on an inclined plane

 

Related Topics

1. Defining Kinematics & Dynamics
2. Motion in one dimension
3. Motion in two dimension
4. Distance & Displacement
5. Average Speed and Velocity
6. Acceleration
7. Equation of Motion in Straight Line
8. Equation of Motion in Inclined Plane
9. Relative Velocity
10. Representation of graphs(variation in displacement, velocity and acceleration in different types of motion)

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