Motion of particle in an electric field

[Falken_47]

Homework Statement

Suppose a proton is at rest and at the origin of some coordinate system. Then, electric field of E(r) = E₀ X-hat is turned on. What is the position of proton at time t and then its velocity?

Homework Equations

E(r) = E₀ X-hat

F_proton = e * E(r)

The Attempt at a Solution

By using, F_proton = e * E(r), I obtained

ma = e * E₀ X-hat
a = ( ( e * E₀ ) / m ) X-hat

therefore, integrating the equation, I obtained

v = ( ( e * E₀ * t ) / m ) X-hat
x = ( ( e * E₀ * t² ) / ( 2 * m ) ) X-hat

(note that constant of integration is ignored because initial v and x is zero)

So, the above answer should be correct right? And when we graph it we would have a parabola for x and a line of constant slope for v which is then similar to the model of an object under constant acceleration?

I'm just making sure since the answer to the question is pretty much straightforward that I'm afraid I'm missing something.

Thank you in advance!

 

[SammyS]

Homework Statement

Suppose a proton is at rest and at the origin of some coordinate system. Then, electric field of E(r) = E₀ X-hat is turned on. What is the position of proton at time t and then its velocity?

Homework Equations

E(r) = E₀ X-hat

F_proton = e * E(r)

The Attempt at a Solution

By using, F_proton = e * E(r), I obtained

ma = e * E₀ X-hat
a = ( ( e * E₀ ) / m ) X-hat

therefore, integrating the equation, I obtained

v = ( ( e * E₀ * t ) / m ) X-hat
x = ( ( e * E₀ * t² ) / ( 2 * m ) ) X-hat

(note that constant of integration is ignored because initial v and x is zero)

So, the above answer should be correct right? And when we graph it we would have a parabola for x and a line of constant slope for v which is then similar to the model of an object under constant acceleration?

I'm just making sure since the answer to the question is pretty much straightforward that I'm afraid I'm missing something.

Thank you in advance!

That all looks good.

Technically, you're not ignoring the constants of integration. You have actually given the justification for them to be zero.

 

[Falken_47]

Ok, thank you very much for the reply!