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Understanding the Concept of Acceleration

Approaching the study of acceleration and it’s relation with other physical quantities.

The problems of physics are more than exercises of the intellect. Many people, including some physicists, think otherwise.

In reality, physics is our second nature. The physical reality, as we perceive it, is so apparent that most people don’t even think about it.

For example, people have always known that when you throw something up, it goes down. But it wasn’t until Newton discovered it that it came into the domain of formal thought.

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The other great scientist credited for the development of this concept is Galileo Galilei. Galileo painstakingly recorded the motion of objects rolling down a plane. He figured out that the distance covered by the objects was proportional to the square of the time taken. 

What it means is that if you take the time and multiply it by itself, this quantity increases in the same ratio as the increase in distance.

The concept of acceleration

Gravitation is a form of acceleration, and acceleration is one of the fundamental concepts in physics. When we say that a body is moving at a certain speed, we mean that it is covering a certain distance at a specific time. 

When we say a body is accelerating, we mean that the body travels at a different speed than before, and the acceleration is the speed it acquires at a specific time.

The mathematical expression is a=Δv/Δt, where a is acceleration, Δv is the change in velocity and Δt change in time. Since velocity itself is expressed as v=Δs/Δt, where Δs is a change in distance and Δt is a change in time, we can deduce the acceleration equation to a=Δs/Δt2.

The equation shows that, for constant acceleration, distance is directly proportional to time squared. This relation between time and distance is what Galileo discovered and tried to explain.

The word ‘accelerate’ comes from Latin, ‘accelerare,’ meaning ‘to hasten.’ It is formally defined as the rate of change of velocity with respect to time.

Acceleration as a vector quantity

It can be noticed how the word ‘velocity’ is used instead of speed. In physics, these near-synonyms are different. Velocity is something known as a vector quantity. 

It means that the quantity of speed is attributed to the motion in one particular direction.

To understand this distinction, consider what happens when you fly a paper plane in the wind. There is one direction to the wind and another direction in which you throw the plane.

However, the resultant path is in neither direction. It is the result of both these things combined.

In this condition, velocity is not just a measure of how much distance the paper plane covers, but how much distance it covers in a particular direction.

Similarly, acceleration is not just a measure of the change in velocity, but also a change in the direction of motion.

A vector quantity is indicated by a bar or an arrow above the symbol. It has its own mathematical system.

What causes acceleration?

Most people identify acceleration with driving. When you press the accelerator, the car moves faster. 

We know this is achieved by the combustion of fuel in the internal combustion engines. It is an elaborate process of how the energy of fossil fuels leads to motion, and its physics is equally tricky.

The combustion leads to kinetic energy that gives rise to a force. The force materializes as a change in momentum, which is another concept described by Sir Isaac Newton. 

Here, momentum is the product of mass and velocity. This relation is expressed mathematically as ‘p=mv.’ One of its properties is that momentum in a closed system remains conserved.

According to Newton’s second law of motion, “Force is equal to the change in momentum per change in time. For a constant mass, force equals mass times acceleration.”

Mathematically, the equation is F=ma, which implies that a=F/m.

Thus, the higher the force, the higher the acceleration; the higher the mass, the slower the acceleration.

It is prudent here to describe mass. Mass is the amount of matter contained in a substance. It is what is commonly known as the weight of a body. But in scientific terms, weight is considered as the force by which a body is attracted by gravity.

Obviously, the weight of a body is related and proportional to the mass of a body.

Another related concept is retardation or slowing down. It is difficult to picture slowing down as technically an acceleration.

But retardation is just acceleration in the opposite direction, i.e., negative acceleration.

Types of acceleration

Linear acceleration:

An object moving in a straight line can only accelerate by a change in its velocity. This acceleration is known as linear acceleration.

As discussed above, it may be positive or negative, depending on the direction.

Curvilinear acceleration

In curvilinear motion, which is the motion happening in a non-linear plane or along a curve, there is a constant change in direction. A typical example of this is circular motion or motion along a circular path.

The acceleration, in this case, is called curvilinear acceleration. Acceleration, in a practical environment, maybe a combination of the two. 

Conclusion

The fundamentals of physics are not dry concepts. They have emerged from years of research and observations, first by early philosophers and later scientists. Philosophers believed that these laws could define not just objects and mechanics but could also be extended to understand the universe and life itself.

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Science is a systematic approach to some of the problems that concerned these philosophers. But it is not absolute.

New theories come every now and then and replace older ones. What’s important is the method and its application.

In a way, we’ve built today’s world- the tech-driven world- on top of these principles. Thus, the belief that physics would one day define the world is a self-fulfilling prophecy.

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