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# How Do I Solve Motion in a Plane Problem Easily?

In Physics, the concept of motion is introduced and discussed in the broad heading of Kinematics. It is introduced in class 11th and is a very interesting topic. To be precise, the concept of motion in a plane, for school level education, is limited to particle kinematics. This begs the questions, as to ‘What is Kinematics?’ Kinematics is a subset of the broader universal set of Physics and is listed under the heading of classical mechanics. Kinematics deals with the motion of various bodies (points, objects or systems) without taking into account the forces producing this motion. It can be also be understood to be the study of ‘geometry of motion’. Good mathematical understanding of Calculus, Algebra, Trigonometry and Coordinate Geometry are needed for a deep level understanding of kinematics. The method to solve any problem of kinematic is pretty straightforward. The first step to solving any problem of kinematics is to define the geometry of the system. The next step is to determine all the initial conditions pertaining to parameters such as position, velocity or acceleration of the body. The next step included, the determination of the unknowns by taking into account the initial conditions and other arguments. Kinematics has a wide range of application. In the field of astrophysics, the concepts of kinematics are used to explain the motion of the heavenly bodies. In engineering, it is used to explain the motion of systems such as engine, machines etc.

The topic of motion of particles from the subject Physics is also interesting because here not only magnitude but also direction of the particle plays an important role. Therefore, vectors and its computation is necessary to solve doubts & problems related to particle kinematics. Thus, one must understand that there are two kinds of physical quantities, namely, scalar and vectors. A scalar quantity is a quantity that only has a magnitude, whereas a vector quantity has magnitude as well as direction. Speed is a scalar quantity however, velocity is a vector quantity. There is a difference in the understanding of a train running at a speed of 100 kmph and a train headed due east with a speed of 100 kmph. Former is scalar while latter is a vector quantity. It is important to brush up the mathematical operations of vectors along with graphical representation of vectors to study kinematics. Parameters such as displacement, velocity and acceleration are important. In addition, there also exists concepts of instantaneous and average quantities in kinematics. Instantaneous velocity and average velocity are not the same thing.

Motion in a plane is also discussed as a motion happening in two dimensions, such as motion in a circle (circular motion), projectile motion. To analyse this kind of motion, one must take the origin of the 2D plane as the reference point and perform the analysis. Motion in a plane denotes to the point where we study motion in two dimensions as a plane consists of only two dimension. Following generalized equations are derived for motion in a plane.

v = u+at

s = ut+1/2 at²

v= u² + 2as

Where,

• v = terminal velocity of the particle
• u = initial velocity of the particle
• s = displacement suffered by the particle
• a = acceleration of the particle
• t = the time interval during which the particle is in motion.

Let us take a numerical problem to see how these formulae can be applied. Let us consider a body at rest. It begins to move in a straight line due East, with a constant acceleration of 10 ms-2. Determine the displacement of the body and the final velocity of the body if it moves with the constant acceleration for one minute.

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Now, by looking at the problem, we first need to study the geometry of the system. If we imagine the two dimensional space, we can assume the particle to be at rest at origin. The problem specifies that it is moving in straight line due East, this means it is moving in the X direction alone. Also, it is moving with constant acceleration. The motion happens for one minute, that is, 60 seconds.

### Learn how to solve the below Question:

An athelete completes one round of a circular track of radius R in 40 seconds. What will be the displacement at the end of 2 min. 20 second?

Let us look at the data and initial conditions,

• Initial velocity (u) = 0 m/s
• Time interval (t) = 60 s
• Acceleration (a) = 10 ms-2
• Displacement (S) =?
• Terminal velocity (v) =?

Substituting the value to get the displacement, we can use the formula

s = ut + 1/2 at²

We can calculate the displacement S = 18000 m = 18 km

To Determine the final velocity, we can use the formula,

v = u + at

Substituting the values, we get final velocity v= 600m/s

In order to solve problems of motion in a plane, one must practice a lot of problems. One can begin studying by referring to the NCERT class 11th book for physics and solving every problem there. Remember, practice is the key to success.

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