What Is the Final Velocity of a Particle Under a Time-Dependent Force?

[Alex Wik]

Homework Statement

A particle with the mass m moves in one dimension. It is in rest when t=0 and affects later after a by The time dependent force. F(t) =F0*e^(-at) where F0 and a is constants. When The time is really big The particels velocity get close to a spesific value. What is it?

Homework Equations

F(t) =F0*e^(-at)
I= delta(p)

The Attempt at a Solution

[/B]
I have tried to take The intergrals of both sides. F(t) =F0*e^(-at)--> I (impulse) = integrals from 0 to infinite( F0*e^(-at) /-at) But later on I can not seem to be a solve this general intergrals. And then i need to solve The velocity from the impulse.

 

[Phylosopher]

Sorry, I posted a wrong answer just a moment ago...

Do you know what is the integral of ∫ e^x dx ?

 

[Alex Wik]

Sorry, I posted a wrong answer just a moment ago...

Do you know what is the integral of ∫ e^x dx ?

Yes. It is e^x+C

 

[Phylosopher]

Yes. It is e^x+C

Very good. Now, what can you do for e^-at so that it looks more like e^x ?

 

[LCKurtz]

Please do not post in boldface type.

Homework Statement

A particle with the mass m moves in one dimension. It is in rest when t=0 and affects later after a by The time dependent force. F(t) =F0*e^(-at) where F0 and a is constants. When The time is really big The particels velocity get close to a spesific value. What is it? [/B]

Do you mean for both the $a$ values I put in red to be the same?

Homework Equations

F(t) =F0*e^(-at)
I= delta(p) [/B]

The Attempt at a Solution

What is $p$? What impulse?

I have tried to take The intergrals of both sides. F(t) =F0*e^(-at)--> I (impulse) = integrals from 0 to infinite( F0*e^(-at) /-at) But later on I can not seem to be a solve this general intergrals. And then i need to solve The velocity from the impulse.

 

[Mark44]

Please do not post in boldface type.

Now fixed in the OP.

have tried to take The intergrals of both sides. F(t) =F0*e^(-at)--> I (impulse) = integrals from 0 to infinite( F0*e^(-at) /-at) But later on I can not seem to be a solve this general intergrals.

"Intergrals" is not a word -- the correct spelling is integrals.

 

[vela]

I have tried to take The intergrals of both sides. F(t) =F0*e^(-at)--> I (impulse) = integrals from 0 to infinite( F0*e^(-at) /-at) But later on I can not seem to be a solve this general intergrals. And then i need to solve The velocity from the impulse.

If I understand what you wrote, you said
$$\text{Impulse} = \int_0^\infty F(t)\,dt = \int_0^{\infty} \frac{F_0 e^{-at}}{-at}\,dt.$$ Is that what you meant?

 

[Apashanka]

particle with the mass m moves in one dimension. It is in rest when t=0 and affects later after a by The time dependent force. F(t) =F0*e^(-at) where F0 and a is constants. When The time is really big The particels velocity get close to a spesific value. What is it?

v(t)=-F₀/(ma)exp(-at)+c
for large t clearly v=c.
c can be determined from the boundary condition at t=0 which is F₀/ma