You are at rest, and a spaceship travels at constant velocity behind you at 1.00
km/s. You wish to dock to this spaceship - in order to do this, you need to be
at the same velocity and position as the spaceship. You can accelerate yourself
at a rate of 30.0 m/s2.

a. How long does it take you to reach the same velocity as the spaceship?

b. How far have you travelled from your starting point to the point where
you reach the same speed as the spaceship?

c. Using your answers from parts a and b, how far behind you should you wait
for the spaceship to be before beginning to accelerate? (Hint: determine
the initial position of the spaceship to be at the same position as you are
when you are at the same velocity).

d. Suppose instead you can accelerate at a non-constant acceleration, given
by function a(t) = (5.00m/s3)t. Using a similar approach to parts a, b,
and c, determine how far behind you the spaceship should be before you
begin accelerating. (Hint: use integrals to get the velocity and position
functions for yourself).