- #1

Samkiwi

- 16

- 1

- Homework Statement:
- I'm having trouble finding the proof of the relativistic acceleration formula starting from the velocity formula, I've been working on it for a long time but I can't solve this question. :)

- Relevant Equations:
- electromagnetism and relativity

It is an electron initially pushed by the action of the electric field. The vectors of force and velocity are parallel to each other.

Here's the question

A possible expression of speed as a function of time is the following:

$$v(t) = \frac{At}{\sqrt{1 + (\frac{At}{c})^2}}$$

where is it $$A =\frac{qE}{m}$$

Taking into account that [2] can be written in the equivalent form.

$$\frac{dv}{dt}=\frac{qE}{m}(1-\frac{v^{2}}{c^{2}})^{-\frac{3}{2}}[3]$$

verify by deriving and substituting that the function v (t) defined by [2] satisfies [3]

Here's the question

A possible expression of speed as a function of time is the following:

$$v(t) = \frac{At}{\sqrt{1 + (\frac{At}{c})^2}}$$

where is it $$A =\frac{qE}{m}$$

Taking into account that [2] can be written in the equivalent form.

$$\frac{dv}{dt}=\frac{qE}{m}(1-\frac{v^{2}}{c^{2}})^{-\frac{3}{2}}[3]$$

verify by deriving and substituting that the function v (t) defined by [2] satisfies [3]