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Answer 1

Answer:

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Answer 2

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Newton’s second law establishes a relationship between the force F

acting on a body of mass m and the acceleration a caused by this force.

The acceleration a of a body is directly proportional to the acting force F and inversely proportional to its mass m, that is a=Fm

or

F=ma=md2rdt2.

This formulation is valid for systems with constant mass. When the mass changes (for example, in the case of relativistic motion), Newton’s second law takes the form

F=dpdt,

where p is the impulse (momentum) of the body.

In general, the force F can depend on the coordinates of the body, i.e., the radius vector r , its velocity v , and time t :

F=F(r,v,t).

Below we consider the special cases where the force

F

depends only on one of these variables.

Force Depends on Time:

F=F(t)

Assuming that the motion is one-dimensional, Newton’s second law is written as the second order differential equation:

md2xdt2=F(t).

Integrating once, we find the velocity of the body v(t):

v(t)=v0+1mt∫0 F(τ)dτ.

Here we assume that the body begins to move at time

t=0 with the initial velocity

v(t=0)=v0.

Integrating again, we get the law of motion

x(t):x(t)=x0+t∫0 v(τ)dτ , where

x0 is the initial coordinate of the body,

τ is the variable of integration.