All Problems

Relativistic Mechanics

Problem 1.378

A particle of rest mass \(m_{0}\) starts moving at a moment \(t=0\) due to a constant force \(\mathbf{F}\). Find the time dependence of the particle's velocity and of the distance covered.

Reveal Answer
v=Fct/mn2c2+F2t2,l=(m0c2/F)2+c2t2m0c2/Fv=F c t / \sqrt{m_{n}^{2} c^{2}+F^{2} t^{2}}, \quad l=\sqrt{\left(m_{0} c^{2} / F\right)^{2}+c^{2} t^{2}}-m_{0} c^{2} / F