A spaceship approaches Starbase Beta with an initial velocity moving in the +x direction. The ensign sets the ship's computer to initiate a braking program starting at time t = 0. After this time the computer controls the ship's x-velocity according to until the ship docks at the Starbase. The numerical values of the constants are b = 100 and α = 0.1 (SI units).
(a) Sketch vx(t). What are the units of b and α? Interpret what they represent physically.
(b) Find ax(t) and sketch it. When is the maximum acceleration and what is its value (magnitude)?
(c) Find x(t) and sketch it. Assume that the position of the spaceship is defined to be at x = 0 at t = 0. How far has the ship traveled after it has come to rest?