Consider a particle moving along the x-axis whose velocity as a function of time is dx_ _ gt dt yi+ g 2 t 2 where g is a constant.

(a) does the particle’s speed ever exceed the speed of light?

(b) calculate the components of the particle’s four-velocity.

(c) express x and t as a function of the proper time along the trajectory.

(d) what are the components of the four-force and the three-force acting on the particle?