Why Formulas Alone Cannot Solve Physics Problems


During my twenty years of teaching Physics, I have met countless students who say:

"Sir, I know all the formulas, but I still cannot solve the problem."

This raises an important question:

If formulas are so important, why do students struggle even after memorising them?

KEY IDEA

Physics problems are not solved by memorising formulas. They are solved by understanding the physical situation and then choosing the appropriate mathematical tool.

Physics Is Not Mathematics

There is an important difference between Mathematics and Physics.

In Mathematics, a problem is often solved by applying a known result, theorem, or formula. Once you recognise the pattern, the path to the solution becomes clear.

Physics is different.

A Physics problem first requires you to understand what is actually happening in the physical world. Only then can you decide which mathematical tool, formula, or method should be used.

In other words, formulas do not solve Physics problems. People solve Physics problems by using formulas intelligently.

The difficult part is not the formula itself. The difficult part is choosing the right formula.

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An Example

Consider the following problem:

A projectile is projected with speed u at a certain angle with the horizontal. Find the time after which its velocity becomes perpendicular to its initial velocity.

Many students immediately start searching for equations of projectile motion.

But before writing any formula, let us think about the situation.

Step 1: Understand What Changes

During projectile motion, the velocity of the particle continuously changes because gravity acts on it.

The acceleration remains constant and is directed vertically downward.

Therefore, after time (t), the change in velocity has magnitude (gt) and is directed downward.

Step 2: Build the Velocity Diagram

The final velocity can be obtained by adding the change in velocity to the initial velocity.

Since velocity is a vector quantity, we must perform vector addition.

The problem tells us that the final velocity is perpendicular to the initial velocity. This information allows us to construct the vector diagram shown below.


At this stage, no formula has solved the problem.

What solved the problem was:

  • Understanding projectile motion

  • Understanding acceleration

  • Understanding change in velocity

  • Understanding vector addition

Only after these ideas are clear do we use mathematics to complete the solution.

Step 3: Use Mathematics

Now the triangle formed by the vectors can be solved using trigonometric relations.

At this point, the formula is useful because we already understand the underlying physics.

The Real Lesson

This example teaches us an important lesson.

Students often believe that success in Physics depends on memorising more formulas.

My experience suggests otherwise.

Success in Physics depends on developing the ability to:

  • Visualise the physical situation

  • Identify the relevant concepts

  • Construct diagrams

  • Choose the appropriate mathematical tool

  • Apply formulas in the correct context

Formulas are important, but they are only tools.

A mechanic is not successful because he owns many tools. He is successful because he knows which tool to use and when to use it.

Physics works in exactly the same way.

The next time you get stuck in a problem, do not ask:

"Which formula should I use?"

Instead ask:

"What is really happening here?"

That question is often the starting point for a correct solution.


Takeaway

The real challenge in Physics is not remembering formulas...

Continue Learning

About the Author

Sutikshna Mishra is a Physics educator with more than 20 years of teaching experience. He mentors students preparing for Physics Olympiads, JEE Advanced, and other competitive examinations through concept-based learning and problem-solving.

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