[ukiecutie13]

Analyze the motion of a rock dropped in water in term of its speed and acceleration. Assume that a resistive force acting on a rock increases as the velocity increases?

please help... I don't understand this =[

A sky diver falls through the air. As the speed if the sky diver increases, whtat happens to the shy diver's acceleration? What is acceleration when the sky diver reaches terminal speed?

[enigmagnetic]

Acceleration goes to zero during terminal speed. Hence the "terminal" speed name. You have to look at water as very small pieces of matter. Water is made of molecules which are very small particles. Remember the ball zone at McDonald's play area back when you where a kid? Remember how when you jumped into the ball pit it slowed you down? The ball pit kind of had you float on top of all the balls. That's an analogy for the reason water slows you down. You're basically moving against a bunch of matter. If you were not being "held" back by such matter than you would have unrestricted motion. Well when it comes to matter that is because there is always gravity and that is a whole other story indeed. The same reason air slows you down to a terminal speed, is the same reason water slows your motion. Now

[tjsail]

"rock dropped in water in term of its speed and acceleration": Assume you held the rock at the surface so the rock was fully submerged, and then released it. The rock has weight. That's a force. Newton's 2nd says that if there is a net force, Fnet, on the rock it must accelerate based on the equation
F = m*a

As the rock accelerates, it gains velocity according to the equation
V = a*t

But as the rock gains velocity, it experiences a force resisting the motion. (This force is like the wind in your face if you bicycle fast downhill. The force of the wind resists your velocity.) So the rock has 2 forces acting on it now: weight downward and drag from the water is a force upwards. So that means that the net force, Fnet, has decreased.
Fnet = Weight - WaterDrag = m*a

So the acceleration starts decreasing as soon as the velocity starts increasing. When the velocity gets high enough, WaterDrag will be equal to the Weight. Therefore Fnet will be zero. When Fnet is zero the acceleration will be zero. So the velocity reaches a certain value (terminal speed) and doesn't change anymore -- till it hits the bottom of the lake.

The same thing happens to the sky diver.