• LOGIN
  • No products in the cart.

Profile Photo

Position of a Particle

A particle of mass m is subject to a force $$ F(t)=me^{-bt}$$. The initial position and speed are zero. Find \(x(t)\).

Solution: In the given problem $$ \ddot{x}=e^{-bt}$$
Integrating this with respect to time gives $$ v(t)=-\frac{e^{-bt}}{b}+A $$ ( A is the constant of integration)
We integrate again with respect to x.
$$ x(t)=\frac{e^{-bt}}{b^2}+At+B$$ ( B is the constant of integration)
The initial condition \( v(0)=0\),gives \(\frac{-1}{b}+A=0\) $$\Rightarrow A= \frac{1}{b}$$
The intial condition $$ x(0)=0$$, gives $$\frac{1}{b^2}+B=0$$ $$\Rightarrow B=-\frac{1}{b^2}$$

Hence,

$$ x(t)=\frac{e^{-bt}}{b^2}+\frac{1}{b}t-\frac{1}{b^2}$$

No comments, be the first one to comment !

Leave a Reply

Your email address will not be published. Required fields are marked *

© Cheenta 2017

Login

Register

FACEBOOKGOOGLE Create an Account
Create an Account Back to login/register
X