# Differential Equation Involving Newtons Law of Motion

• SparkyEng
In summary, to find the position function using the initial conditions of t=0 for all constants, use the reverse product rule and solve the equation mv'=-gm-kv using separation of variables.
SparkyEng

## Homework Statement

mv'=-gm-kv

Find the position function using the initial coniditions of t=0 for all Constants

## Homework Equations

Reverse product rule

## The Attempt at a Solution

My attempt is on my white board. Its attached as a picture.

#### Attachments

• photo.jpg
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SparkyEng said:

## Homework Statement

mv'=-gm-kv

Find the position function using the initial coniditions of t=0 for all Constants

## Homework Equations

Reverse product rule

## The Attempt at a Solution

My attempt is on my white board. Its attached as a picture.

You've got some problems there. For example the integral of vdt isn't equal to v*t. v is a function of t. Why don't you try to solve mv'=-gm-kv using separation of variables?

From mv'= m dv/dt= -gm- kv, you can get m dv/(gm+kv)= -dt, separating the variables "v" and "t". Integrate both sides of that.

## 1. What is a differential equation involving Newton's Law of Motion?

A differential equation involving Newton's Law of Motion is a mathematical equation that describes the relationship between the motion of an object and the forces acting upon it, using the principles of Newton's Laws of Motion.

## 2. What are Newton's Laws of Motion?

Newton's Laws of Motion are three physical laws that describe the relationship between an object's motion and the forces acting upon it. The first law states that an object at rest will remain at rest and an object in motion will remain in motion at 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 upon it and inversely proportional to its mass. The third law states that for every action, there is an equal and opposite reaction.

## 3. How are differential equations used in Newton's Law of Motion?

Differential equations are used in Newton's Law of Motion to mathematically model the motion of an object based on the forces acting upon it. By solving the differential equation, we can determine the position, velocity, and acceleration of an object at any given time.

## 4. What is the difference between a differential equation and a regular equation?

A differential equation involves derivatives, which represent the rate of change of a variable, while a regular equation only involves the variables themselves. This means that a differential equation describes the relationship between a function and its derivatives, while a regular equation only describes the relationship between different variables.

## 5. Why are differential equations important in physics and engineering?

Differential equations are important in physics and engineering because they provide a mathematical framework for describing and predicting the behavior of physical systems. They are used to model a wide range of phenomena, from the motion of planets to the flow of fluids, and are essential for understanding and solving complex problems in these fields.

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