- #1
Physicsphysics
- 17
- 2
- Homework Statement
- A particle is moving along x, uniformly accelerated at a=g=constant.
(a) find x and t as a function of proper time (provided at t=0, x=0 and v=0)
Hint: (now a and u are 4-vectors) consider u and a. What are a.a, u.u and a.u? Use these to find the particle's 4-velocity and integrate to find position.
- Relevant Equations
- Still 4-velocities
u.u=1
a.u=0
u=(γ,γv)
a=(γ[SUP]4[/SUP]v.a, γ[SUP]2[/SUP]a + γ[SUP]4[/SUP](v.a)v)
On the right hand side, v and a are three vectors
I tried finding a.a (four vector inner product) and I got to γ4{(v.a)2(1-γ4v.v - 2γ2) - a.a}, where again a and v are three vectors on the rhs (sorry to be confusing). a.a = g2 since it's a constant.
I have no idea where to go from here to find the time and position. Please help!
I have no idea where to go from here to find the time and position. Please help!