Answer: 
Explanation:
A direct proportionality means a linear relationship between two variables and rate of change means an application of derivatives. Hence, the mathematical model is:

We will start from the definition of power in terms of the Force. Power could be described as the change of energy in an instant of time. Considering that Energy is the product between the Force and the distance traveled we would arrive at the expression


Here,
F = Force
h = Height
t = Time
As there is no external force, apart from the force of gravity, and this, is constant during the course of the object we will also have to be constant power and therefore this during its course will be the same. The correct answer is (1)
1) Right answer: 
Gravity is a physical force with which the Earth exerts on all bodies towards its center due to the fact its mass is greater than the bodies on its surface.
Nevertheless, it is important to note that this value is not the same in all the points of the planet, that is why an average value is used, which is
.
2) Right answer: 
The Average Velocity Formula is:

Where
is the Initial Velocity and
is the Final Velocity.
Knowing this, let's apply the formula:


3) Right answer: 


4) Right answer: 


Answer: Total work done on the block is 3670.5 Joules.
Step by step:
Work done:

With F the force, d the displacement, and theta the angle of action (which is 0 since the block is pushed along the direction of displacement, and cos 0 = 1)

Given:
F = 75 N
m = 31.8 kg
Final velocity 
In order to calculate the Work we need to determine the displacement, or distance the block travels. We can use the information about F and m to first figure out the acceleration:

Now we can determine the displacement from the following formula:

Here, the initial displacement is 0 and initial velocity is also 0 (at rest):

Now we still have "t" as unknown. But we are given one more bit of information from which this can be determined:

(using vf as final velocity, and tf as final time)
So it takes about 6.44 seconds for the block to move. This allows us to finally calculate the displacement:

and the corresponding work:
