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impulse or linear momentum or translational momentum is the
product of the mass and velocity of an object:
 
p  m v  . (3.13)

To change the impulse of an object on dp the force F has to act during
time dt
 
pd  F  dt
(3.14)
hence 
 p d
F  (3.15)
dt .

This formula is Newton's formula and as he stated it himself:

The alteration of motion(linear momentum ) is ever proportional
to the applied motive force ; and directed on the straight line in
which that force is applied
All previous definitions of second Newton's law are up-to-date

definitions
3.4 Newton's Third Law
To every action there is always an equal and opposite reaction or

the forces of two bodies on each other are always equal and are
directed to the opposite side
From a mathematical point of view,
Newton's third law is a one-

dimensional vector equation
 
F   F (3.16)
 12 21
where F force that acts on the
Figure3.2 12
first body due to the second body ,

F - force that acts on the second
21
body du to first one (fig.3.2). In spite of the fact that these forces are
equal, resulting action is not zero, because they are applied to different
bodies. If you press a stone with your finger, the finger is also pressed

by the stone. This law is sometimes referred to as the action-reaction
 
law, withF called the "action" and F the "reaction". The action and
21
12
the reaction are simultaneous. Sometimes not quite understanding
Newton's third law сan result in paradox. Suppose a horse draws a
sleigh as presented in fig. 3.3. According to Newton's third law, force
 
F that acts on the horse due to the sleigh is equal to F -force that
12
21
acts on the sleigh due to the horse. Why does the sleigh move? ?The

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