- #1

- 177

- 13

## Homework Statement:

- The momentum ##p## of an electron at speed ##v## near the speed ##c## of light increase s according to the formula ##p=\gamma mv##, where ##\gamma = \frac{1}{\sqrt{1-v^2/c^2}}##; m is a constant (mass of an electron). If an electron is subject to a constant force F, Newton's second law describing its motion is: $$\frac{dp}{dt}=\frac{d}{dt} \gamma mv=F$$. Find (a) v(t) and show that v approaches c as t approaches infinite. (b) Find the distance traveled by the electron in time t if it starts from rest.

## Relevant Equations:

- For ##dy/dx = c##, the solution is $$y=\int {c dx}$$

$$p=\gamma m v$$

$$F = \frac {md (\gamma v}{dt}$$

$$\int{F dt} = \int{md (\gamma v}$$

$$F t= \gamma mv$$

At this step, I don't know how to make v as explicit function of t, since gamma is a function of v too. Thankss

$$F = \frac {md (\gamma v}{dt}$$

$$\int{F dt} = \int{md (\gamma v}$$

$$F t= \gamma mv$$

At this step, I don't know how to make v as explicit function of t, since gamma is a function of v too. Thankss