# Easy problem, but no idea how to solve it?

• Gramsci
In summary, when encountering an easy problem without knowing how to solve it, it's important to analyze and break down the problem, look for patterns and examples, and seek guidance from others. To improve problem-solving skills, practice and try different approaches, and utilize critical thinking to evaluate information and find creative solutions. If you get stuck on an easy problem, take a break, seek help, and remember that problem-solving takes time and practice to master.
Gramsci

## Homework Statement

A motorbike with the velocity 40km/h is able to stop at a distance, D, when it brakes with maximal deacceleration. At what distance will a car with a velocity of 60 km/h stop?

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## The Attempt at a Solution

I was trying to solve it through regular equations such as at^2=distance, but there seems to be too many unknowns. Any ideas?

Use v^2 - u^2 = 2as. Find a in terms of D. Here u = 40 km/hr and v = 0. Use this a and find the distance for 60 km/hr using the above equation.

I understand your frustration when faced with a problem that seems easy but is difficult to solve. In this case, the key to finding a solution lies in understanding the concept of kinetic energy and its relationship to velocity and braking distance.

First, let's start with the basic equation for kinetic energy: KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity. This equation tells us that an object with a higher velocity will have a higher kinetic energy.

Next, let's consider the concept of work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done on the motorbike and the car would be equal when they come to a stop, as they both have the same initial kinetic energy (since they have the same mass and the same velocity of 40 km/h).

Now, we can use the work-energy theorem to solve for the braking distance of the car. The work done on the car can be expressed as F * D, where F is the force of braking and D is the braking distance. This work must be equal to the change in kinetic energy, which we know is the same as the kinetic energy of the motorbike. Therefore, we can write the equation as:

F * D = 1/2 * m * v^2

We know that the mass and velocity of the car are higher than that of the motorbike (m and v are both greater for the car). Therefore, the force of braking (F) must also be greater for the car to have the same kinetic energy as the motorbike. This is why the car is able to stop at a shorter distance than the motorbike.

To solve for D, we just need to rearrange the equation and plug in the values for mass and velocity of the car:

D = 1/2 * m * v^2 / F = 1/2 * m * v^2 / (m * a)

Where a is the acceleration or deacceleration of the car, which we can calculate using the equation a = (v^2 - u^2) / 2s, where u is the initial velocity (60 km/h) and s is the stopping distance (which we are trying to find).

Plugging in the values, we get:

D = 1/2 * 60 km/h

## 1. What should I do if I encounter an easy problem but have no idea how to solve it?

If you encounter an easy problem but have no idea how to solve it, the first thing you should do is take a step back and analyze the problem. Break it down into smaller, more manageable parts and try to identify any patterns or connections. You can also try to find similar problems or examples online to get a better understanding of the problem and potential solutions.

## 2. How can I improve my problem-solving skills?

To improve your problem-solving skills, practice is key. Attempt to solve a variety of problems and challenges, and don't give up if you encounter difficulties. Additionally, try to approach problems from different angles and seek feedback from others. It can also be helpful to learn new problem-solving techniques and strategies through books, classes, or online resources.

## 3. What role does critical thinking play in problem-solving?

Critical thinking is essential in problem-solving as it involves analyzing and evaluating information, identifying patterns and connections, and using logic and reasoning to come up with solutions. It also helps in identifying potential roadblocks and finding creative ways to overcome them.

## 4. How can I prevent getting stuck on an easy problem?

To prevent getting stuck on an easy problem, it's important to have a clear understanding of the problem and any relevant concepts. If you find yourself getting stuck, take a break and come back to the problem with a fresh perspective. It can also be helpful to talk through the problem with someone else or try to solve it in a different way.

## 5. What should I do if I still can't solve an easy problem after trying different approaches?

If you have tried different approaches and still can't solve an easy problem, it's important not to get discouraged. Take a break and come back to the problem later. You can also seek help from a teacher, tutor, or fellow scientist for guidance and support. Remember that problem-solving is a skill that takes time and practice to develop.

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