A rock is thrown downward into the water with initial speed of3mkg. The fluid resistance isf=kv.

The rock's position in the water is given by

y(t)=gmk(t+2mk(1ektm))

(4 points) Draw a free body diagram for the rock in the water

a) (4 points) Using the derivative, derive the velocity as a function of time t.

b) (4 points) What is the velocity at timemk?

c) (4 points) What is the rock's positionyat time?

d) (4 points) From the velocity from part a, using derivative derive the acceleration as a function of time t

e) (4 points) What is the acceleration of the rock at time ?