On April 15, 1912 the Titanic sank in the ocean. As it sank, its distance, in meters from the floor of the ocean was measured as $s(t) = 1350 − t\operatorname{ln} t$.

1. If t is measured in seconds, find the velocity of the ship at the time it hit the ocean floor.

   Step 1(a):

   Use the position function to find the time the Titanic hit the ocean floor.

   Step 2(a):

   Evaluate the velocity function at that time.

2. Find the acceleration function $a(t)$. Why isn't the acceleration constant in this situation as it is with dropped objects in the air?

   Hint (b):

   Acceleration is known to be constant on Earth: $−32$ ft/sec$^2$. This constant is often used in problems involving falling objects (like soccer balls). How is a sinking ship different from a falling ball?