# Mathematics differntial equations (acceleration)

• delsoo
In summary, the conversation is about a question in which the asker provided their answer and the given answer, and asked for help in finding their mistake. The respondent provided a summary of the steps taken in solving the problem and pointed out where the mistake may have occurred. They also suggested considering the relationship between velocity and position to find the solution.
delsoo

## Homework Statement

part b (question 1 ) , my ans is -3/2 ... but the ans given is 2/3... i don't know where's my mistake...
http://imgur.com/ZCrnKA8,bu5bblS

## The Attempt at a Solution

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you were given a(t)=3t2-10t
you put dv/dt = a(t) and solved the initial value problem to find v(t) and thus v(2).

in the next part you did fine up to: v.dv = a(t).dx but you cannot take a(t) outside the integration.
since x changes with t, t must be a function of x.

consider: what is the relationship between v(t) and x(t)?

How did you get on?

1 person

## 1. What is a differential equation in mathematics?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It involves the use of derivatives to represent the rate of change in a system.

## 2. How is acceleration represented in a differential equation?

In a differential equation, acceleration is represented by the second derivative of a function. This means that the rate of change of the rate of change of a system is being described.

## 3. How are differential equations used to model real-world systems?

Differential equations are used in many fields of science and engineering to model real-world systems. They can be used to describe the behavior of physical systems such as the motion of objects, the growth of populations, and the flow of fluids.

## 4. What are the different types of differential equations?

There are several types of differential equations, including ordinary differential equations (ODEs), partial differential equations (PDEs), and stochastic differential equations (SDEs). ODEs involve a single independent variable, while PDEs involve multiple independent variables. SDEs incorporate randomness and uncertainty into the equations.

## 5. What is the significance of solving a differential equation?

Solving a differential equation allows us to understand the behavior of a system over time and make predictions about its future state. It also helps us to find optimal solutions to problems and make informed decisions in various fields of study.

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