Kinematics

What is Kinematics?

Kinematics is the study of motion. This is literally what the word means: Kinesis (motion) + tics (the study of. Think mathematics, politics etc.).

The kinematics you learn in your intro physics class is the study of position, velocity, and acceleration. On the most practical level, kinematics is the study of what happens when you toss a ball. Which means, if you can toss a ball, you can learn kinematics.

Knowing this, you just have to concentrate on the motion of the bodies, and not the bodies themselves. Forget the mass of the bodies, what force caused them moving, why they are moving that way. and just focus on their motion. For example, when I say, “A cricket ball is thrown vertically upwards with an initial velocity 20 m/s from a tower 60 m high”, you just have to visualize a point (pay attention when I say, just a point; Kinematics doesn’t bother about the mass of the bodies) at a height 60 m from ground level going upwards at 20 m/s. Nothing else! Having visualized it, start analyzing its motion. How it goes up, how it decelerates, when it stops in the air, how it starts accelerating downwards and finally when it reaches the ground.

Dissecting the topic

You’d probably get the opportunity to learn kinematics from your school onwards. The basics from your classes 7 and 9, and you could learn it in sort of advanced level from your class 11. From the perspective of competitive examinations, Kinematics is a considerable topic and you should have to expect much more problems from it than other topics. From the JEE perspective the gravity of this topic is approximately 1-2% and from the perspective of NEET is about 2-3%.

In our curriculum, we’ve divided the topic into the 3 main subtopics. They are rectilinear motion, projectile motion (motion in two dimensions) and relative motion.

These topics can be again divided into:

Rectilinear motion

  • Introduction
  • Various quantities used in kinematics
  • Motion with variable acceleration
  • Graphical representation of motion in one dimension
  • A vertical motion under gravity (Freefall)

Motion in two dimension

  • Projectile motion (Oblique and Horizontal)
  • A projectile is thrown on an inclined plane

Relative motion

  • Relative velocity
  • Rain-man Problems
  • River-swimmer problem
  • Relative motion between two projectiles

Remember these words throughout your journey of Kinematics

Position

Where an object is. It’s location. Physics problems will refer to this as x, y, z p, r, ord. Every teacher has their preferences, so learn yours, but for this blog, we will use x and y. We are also often interested in the change in position, known as displacement, which is referred to as Δx, Δy, Δp, Δd or sometimes just x, y, or d to make things confusing. Position and displacement are usually measured in meters or m.

Magnitude and Direction

Use arrows in your diagrams to show directions, and keep an eye on the magnitudes of velocities and accelerations of the bodies to visualize how “quick” they are moving.

Velocity

How fast an object is moving and in what direction: aka how the distance is changing over time. Physics problems will almost always refer to velocity as v. Velocity is usually measured in meters per second or m/s. When velocity is constant, it can be described by the equation v=Δx/Δt (the change in position divided by the change in time).

Acceleration

How the velocity of the object is changing. If a Ferrari goes from 0 to 60mph in 2.4 seconds then it is accelerating. If the driver freaks out and crashes into a wall that stops the car, then it has also accelerated. Acceleration is always referred to as ‘a’ and is measured in meters per second per second, or m/s2.

When acceleration is constant, it can be as described by the equation a=Δv/Δt (the change in position divided by the change in time). You might notice that this equation is very similar to the equation for velocity. That is not a coincidence: it reflects the vast underlying physics that determines everything in the world.

Scalars and Vectors

The significance of ‘direction’ can be seen in the difference between velocity and speed. In physics, speed is a pure scalar or something with a magnitude but no direction — such as 5 m/s. 5 meters per second does not tell us which way the object is moving. It gives us no clue about the direction. All that we know from the speed is the magnitude of the movement. On the other hand, velocity, in Physics, must be expressed as a vector with both a magnitude and a direction. For instance, 5 m/s Eastward is a velocity because it tells you the magnitude of the movement, 5 meters per second, as well as the direction which is eastward.

Points to remember when you’RE approaching Kinematics

  • Avoid being too mathematical in approach at first. Physics is the understanding of real-life physical phenomena – start there only. Try to find a real life analogy for every problem or concept.
  • Theory portions of kinematics are very less compared to the other topics in physics. You can revise it in less than an hour. So pay more attention to problems.
  • Draw diagrams, always. Even though it may seem really obvious, try to sketch the problem.
  • Learn to use the equations of motion – how and where to apply them – and their limitations with proper sign conventions. These equations are necessary and sufficient for creating the mathematics of the problems. Solving this mathematics is not a problem at all, and you will learn the techniques and tools with time and practice.
  • Be extremely comfortable with vectors. Always try to identify the most appropriate way to resolve the vectors into perpendicular components. This creates the basis of the 2-D motion.
  • Solve as many types of projectile problems as possible. While solving projectile motion, avoid simply putting values in the formulae and calculate the answers. Instead, start every problem from scratch, and derive the expressions needed. Use these derived expressions to find your answers.
  • Besides projectile motion, pay proper attention to circular motion and constrained motion. They have too many applications for other problems as well
  • While analyzing relative motion, be the observer. Stand aside, or move with the objects and try to observe.
  • Lectures from teachers are like waterfalls – pure but constrained. Books are like oceans – saline but vast. Assist your video lectures with books. Refer to them after the video lectures wherever needed.
  • Kinematics is the very first step of the mechanics and hence is important. But once you will complete dynamics and work-energy, you will have spent enough time with mechanics to mix and bifurcate things wisely and revisit the topics with more understanding.
  • All-in-all, repeat the theory portion once again, keeping the above points in mind. Refer to books, if time allows you. And spend more time with a variety of problems rather than solving more number of them.
  • The key to every problem of the whole mechanics is: Keep it simple and always start from the basics.

Hope this article has set you in the right direction towards approaching Kinematics. If you have any questions or thoughts please let us know in the comments below.