I have a few questions............please aid me!...i have ans/sol, and want to know why/not they're right?

Question

1) A 50 kg block rests on a horizontal surface. The coefficient of static friction is 0.50. The coefficient of kinetic friction is 0.35. A force P of 250 N is applied as shown:

[]--------->P

First, can we make conclusions given the data? If not, why not? If so, does the block move and continue to move at a constant velocity?

2) A block is placed on a plane whose angle of inclination is 30 degrees. THe coefficients of static and kinetic friction for the block on the inclined plane are both 0.2. The block........

In this case, would the block accelerate down the plane? If not, what does the block do?

3) Two objects are sliding at the same speed across a wooden surface. The coefficient of kinetic friction between the first object and the surface is twice that between the second object and the surface. The distance traveled by the first object before it stops is S. The distance traveled by the second object is:

Would the answer to this be S/2? Why or why not

Answer 1

1) Yes, we can find out lots of things from this data.
It will move because the force P is greater than the maximum possible force of static friction (which would be 245 N). Once it's moving kinetic friction takes over. Kinetic friction is only 171.5N for this block. Since there is an unbalanced force, the block will have an acceleration, it will not move with a constant velocity.

2)
The component of the block's weight is greater than the force of static friction, so it will slide down. In fact, since the component of the weight is greater than the force of kinetic friction, the block will accelerate down the plane as well.

3)
In each case the acceleration will be (coeff.)x(g). So the acceleration for the first object will be twice that of the second object. From the v-squared kinematic equation (v^2 = vo^2 + 2a(delta)x) you can see that if the acceleration is doubled, the distance must be halved, so the answer will be S/2.