# Newtonian Mechanics - single particle

In summary, the conversation is about finding the force, position, and force as functions of time for a particle with a varying speed based on distance. The solution to part a is F(x)=-ma^2nx^(-2n-1). The individual discussing the problem is stuck on parts b and c and is aware that the "a" in the first formula is not the acceleration, but an arbitrary constant.

## Homework Statement

The speed of a particle of mass [m] varies with the distance[x] as v(x)=ax^(-n). Assume v(x=0)=0 at t=0.
a)Find the force F(x) responsible
b)Determine x(t)
c)Determine F(t)

## The Attempt at a Solution

My solution to part a is F(x)=-ma^2nx^(-2n-1).

## The Attempt at a Solution

Last edited:
F=m(dv/dt), not what you did.

Thats how i got to my answer for part a. I started with that and solved it to get F(x)=-ma^2nx^(-2n-1). This answer was also in the back of my book. I am stuck on part b and c.

The a in your first formula is not the acceleration.
It is just an arbitrary constant.

I know this already too. I put in "a" because I don't have a way to put in alpha.

## 1. What is Newtonian Mechanics?

Newtonian Mechanics is a branch of classical mechanics that studies the motion of objects under the influence of external forces. It was developed by Sir Isaac Newton in the 17th century and is based on three fundamental laws of motion.

## 2. What is a single particle in Newtonian Mechanics?

A single particle in Newtonian Mechanics refers to a point-like object that is small enough to be treated as a single entity. This means that the size and shape of the particle are not relevant, and the focus is on its motion and the forces acting upon it.

## 3. What are the three laws of motion in Newtonian Mechanics?

The first law states that an object at rest will remain at rest, and an object in motion will continue in motion with a constant velocity unless acted upon by an external force. The second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The third law states that for every action, there is an equal and opposite reaction.

## 4. How is the motion of a single particle described in Newtonian Mechanics?

The motion of a single particle in Newtonian Mechanics is described using kinematics, which involves studying the position, velocity, and acceleration of the particle over time. This can be done using mathematical equations such as the equations of motion and the laws of motion.

## 5. What are some real-world applications of Newtonian Mechanics for single particles?

Newtonian Mechanics has many practical applications, such as predicting the motion of objects in projectile motion, analyzing the behavior of objects in orbit, and understanding the motion of particles in a fluid. It is also the basis for many engineering and technological advancements, such as designing bridges, airplanes, and cars.

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