Answer: Hi!
The acceleration of our particle is then a = 4* meters per second square. Also we know that we start at X₀ = O m (i am not sure if you are using a a 0 or a O, but you will see that in this problem it doesn't matter, se i will use a constant O, that can be ani real number as the initial position) and V₀ = 0 m/s.
Ok, we have the acceleration, so if we want the velocity, we must integrate the acceleration over time.
V(t) = ∫ 4*dt = 4*
*t + V₀
where we added the constant of integration, who is the inicial velocity, that we already know that is zero.
and for the position, we must integrate again.
X(t) = ∫ 4**tdt = 4*
*
/2 + X₀
ok, in the part a) we want to know the displacement at 2 seconds.
that is X(2s) - X(0s) = (2000*4 + O) - O meters = 8000 meters.
in the b part we want to know the velocity at 1 second; that is:
V(1s) = 4000*1 m/s = 4000 meters per second.
Given data:
The area of the hydraulic press is,
The applied force is,
The pressing force on the large piston is
Given hydraulic press works on Pascal's law principle.
From the Pascal's law, the equation can be given as,
Here,
is the area of the larger piston.
Substituting the values in the above equation, we get:
Thus, the area of the large piston is
To develop this problem we will apply the Archimedes model. As well as the definitions of Weight based on mass and acceleration. The first in turn will be considered under the relationship of Density and Volume. From the values given we have to:
Since it is in equilibrium, the weight of the object will have a reaction from the water, which will cause the sum of forces between the two objects to be zero, therefore
The value of gravity is canceled because it is a constant
The portion of the object that is submerged corresponds to 82%, while the portion that is visible, above the water level will be 18%