In order to minimize the $g$ forces on you, suppose you decide to accelerate with a constant acceleration such that you reach half the speed of light $(c / 2=1.5 \times$ $10^{8} \mathrm{~m} / \mathrm{s}$ ) at the midpoint of your trip and then start slowing down so you are at rest just in time to dock with the supply vessel at the other end of this solar system.
(a) Draw a single motion diagram showing the speeding-up and slowing-down processes.
(b) In a coordinate system in which you move along the positive $x$ axis, what is the direction and magnitude of your initial acceleration? In other words, is your acceleration positive or negative?
(c) In a coordinate system in which you move along the positive $x$ axis, what is the direction and magnitude of your acceleration while you are slowing down for your rendezvous with the supply vessel? In other words, is your acceleration positive or negative? (Hint: The answer to part (b) and a symmetry argument can save you some effort.)
(d) How long will your overall trip take?
(e) If the Defiant has a mass of $M=2.850 \times 10^{8} \mathrm{~kg}$, what is the thrust force (in newtons) needed to accelerate your starship?
(f) The amount of force you feel being impressed on you by the back of your seat as the starship picks up speed is proportional to your acceleration. A common way to measure typical forces you might feel is to calculate $g$ -forces. This is done by comparing the acceleration you experience to the acceleration you would experience while falling freely close to the surface of the Earth. Thus, you can find $g$ -forces by dividing your acceleration by $9.8 \mathrm{~m} / \mathrm{s}^{2}$. What $g$ -forces would you experience while accelerating in the Defiant?
(g) The maximum sustained $g$ -force that a human can stand is about $3 \mathrm{~g}$. What would happen to you during your leisurely acceleration to half the speed of light?