- #1
Silviu
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- 11
Homework Statement
A particle is moving along the x-axis. It is uniformly accelerated, in the sense that the acceleration measured in its instantaneous rest frame is always g, a constant. Find x and t as a function of the proper time ##\tau## assuming that the particle passes through ##x_0## at time t = 0 with zero velocity.
Homework Equations
The Attempt at a Solution
I am not sure I understand the meaning of "in the sense that the acceleration measured in its instantaneous rest frame is always g, a constant". The way I thought of doing it was ##dt = \gamma d \tau = \frac{d\tau}{\sqrt{1-(gt)^2}}## which implies ##\sqrt{1-(gt)^2}dt=d\tau##, then I integrate and get ##t(\tau)## and a similar reasoning for ##x(\tau)##. However I am not sure this is correct, as this implies that g is constant in the frame where we calculate x and t and I am not sure this is equivalent to what the problem states. Can someone tell me how to approach this correctly? Thank you!