The velocity of the particle as a function of time

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Homework Help Overview

The discussion revolves around determining the velocity of a particle as a function of time, given its acceleration and initial conditions. The problem involves integrating the acceleration function, which includes constants and exponential terms.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to integrate the acceleration function to find the velocity. Some express uncertainty about the correctness of their expressions, particularly regarding the use of exponential terms. Questions are raised about the interpretation of the initial conditions and the formulation of the velocity equation.

Discussion Status

There is ongoing exploration of the problem, with participants questioning the accuracy of their approaches and the formulation of the equations. Some guidance has been offered regarding the structure of the velocity equation, but no consensus has been reached on the correct form or approach.

Contextual Notes

Participants are working under the constraints of the problem statement, which includes specific initial conditions and constants. There is a noted uncertainty about whether the interpretations of the equations are correct.

yesmale4
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Homework Statement
The acceleration of the particle is given by a(t)=bt y + c e kt z.
It is known that at t=0 the velocity of the particle is by v(0)= d x + c/k z and its position is r(0)= c/k2 z.
b, c, d and k are constants.
Relevant Equations
v\left(t\right)=\int \:a\left(t\right)dt
sa.png

this is how i try to solve it:
mm.jpeg


can someone please help me with that because i don't know what I am doing worng here.
 

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Isn't the problem that it should be
Code:
(c/k)*exp(k*t)
(without the ^)?
 
DrClaude said:
Isn't the problem that it should be
Code:
(c/k)*exp(k*t)
(without the ^)?
Thank you very much !
 
yesmale4 said:
Homework Statement:: The acceleration of the particle is given by a(t)=bt y + c e kt z.
It is known that at t=0 the velocity of the particle is by v(0)= d x + c/k z and its position is r(0)= c/k2 z.
b, c, d and k are constants.
Relevant Equations:: v\left(t\right)=\int \:a\left(t\right)dt

View attachment 297864
this is how i try to solve it:
View attachment 297866

can someone please help me with that because i don't know what I am doing wrong here.
Is it telling you it is wrong or is that just what you think?
 

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