This one is tougher! Suppose that a particle experiences a constant force, F = FOE. (a) Show that the acceleration of the particle in the a: direction is given by do F0 '02 3/2 (it m _ c2 I (b) Discuss the signicance of the dependence of the acceleration on the speed. (c) Integrate the acceleration of the charge, assuming that it starts from rest, and show that the velocity as a function of time is given by 1+ 5,1,2 THC (d) What happens to the speed of the a ticle gas t )_> 00-? (e) Show that the position of the particle (starting at 5'; = 0) is given by c2 F t 2 a: t = 1 l D _ 1 . ( ) F0 [ me -| (f) Show that. for small times, such that t me, then we Jet the familiar expression 1 2 13 (t) m Emmat : Where the 11011 relativistic acceleration, em = FU/m. Hint; use the binomial expansion. Does this make sense? (g) What is the distance at very late times, when t _,, 00? Does this make sense