The force of gravity of the body approximately constant, equal to the product of body mass on the acceleration of free fall g. The acceleration of gravity g ≈ 9.8 Newton per kg, or meter per second squared. g is a constant, the value of which varies only slightly for different points of the globe.
By definition, the elementary work of the force of gravity — the product of the force of gravity at an infinitely small movement of the body: dA = mg · dS. The displacement S is a function of time: S = S(t).
To find the work forces of gravity all the way L, you have to take the integral of the elementary work in L: A = ∫dA = ∫(mg · dS) = mg · ∫dS.
If the task is assigned to a function of speed from time to time, the dependence of travel time can be found by integration. For this you will need to know the initial conditions: the initial velocity, coordinates etc.
If the dependence of the acceleration time t, will have to integrate twice, because acceleration is the second derivative of the displacement.
If the task of this coordinate the equation, it should be understood that the movement reflects the difference between the starting and ending coordinates.
In addition to the force of gravity, the physical body can be other forcesaffecting its position in space. It is important to remember that the work is an additive value: the work of the resultant force is equal to the sum of the work terms of forces.
According to the theorem of Kenig, the work force on the moving material point is equal to the increment of the kinetic energy of this point: A(1-2) = K2 - K1. Knowing this, you can try to find the work of the force of gravity through kinetic energy.
To use tabular integration integrals of the elementary functions and rules of integration. Remember that integration is the reverse procedure of differentiation (finding the derivative).