What is zero level and how does it relate to gravitational potential energy?

The nature of potential energy is that the zero point is arbitrary; it can be set like the origin of a coordinate system. That is not to say that it is insignificant; once the zero of potential energy is set, then every value of potential energy is measured with respect to that zero. Another way of saying it is that it is the change in potential energy which has physical significance.

Hope this Helps! 

W = 10.51 J , v = 3.34 m / s

Explanation:

To find the work we use its definition

      W = F .dx

the bold are vectors.  In this case, as the force is in the direction of movement, the product will become algebraic.

       W = F dx

the force that is in the direction of the vector from the origin to the point (0.61, 0.81) this force can be decomposed into its x and y components, where only the x component does work, this component has an initial value of 2, 8 N in position xo = 1.6 and decreases linearly to zero in elections x = 7.5 m

with these data we can find the linear equation of this force

         F = m x + b

the slope is

         m = (2.8 -0) / (0 - 7.5)

         m = -0.373 N / m

       

we find the constant with the starting point

         2.8 = -0.373 0 + b

         b = 2.8 m

the equation of force remains

         F = -0.373 x + 2.8

we substitute in the work equation and integrated

      W = ∫(-0.373 x + 2.8) dx

       W = -0.373 x² / 2 + 2.8 x

We evaluate between the lower limits x = 0 m and upper x = 7.5 m

        W = -0.373 (7.5²/2 - 0) + 2.8 (7.5 -0)

        W = -10.49+ 21

        W = 10.51 J

To find the speed of the train, let's use the relationship between work and the variation of kinetic energy.

       W = ΔK

       W = ½ m v² - ½ m v₀²

       v = √ (v₀ + 2W / m)

       v = √ (1.6 + 2 10.51 / 2.2)

       v = 3.34 m / s