Question H3.6: A constant force is applied to a particle which is initially...
A constant force is applied to a particle which is initially at rest. Sketch a graph that shows the variation of the speed of the particle with time for
(a) Newtonian mechanics;
(b) relativistic mechanics.
In Newtonian mechanics, a constant force produces a constant acceleration, and so the speed increases uniformly without limit, exceeding the speed of light. In relativistic mechanics, the speed increases uniformly as long as the speed is substantially less than the speed of light, and is in fact identical with the Newtonian graph. However, as the speed increases, so does the energy. Because it takes an infinite amount of energy for the particle to reach the speed of light, we conclude that the particle never reaches the speed of light. The speed approaches the speed of light asymptotically. Note that the speed is always less than the corresponding Newtonian value at the same time. Hence we have the graph shown in Figure H3.3.
