According to special relativity, a particle of rest mass m0 accelerated in one dimension by a force F obeys the equation of motion dp/dt = F. Here p = m0v/(1 – v2/c2)1/2 is the relativistic momentum, which reduces to m0v for v2/c2 << 1.
(a) For the case of constant F and initial conditions x (0) = 0 – v (0), find x (t) and v(t).
(b) Sketch your result for v (t).
(c) Suppose that F/mo = 10 m/s2 (≈ g on Earth). How much time is required for the particle ro reach half the speed of light and of 99% the speed of light?