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Newton's second law of motion states the equation below:

[tex]\[ \sum F = ma \][/tex]

where [tex]\(\sum F\)[/tex] is the total external force acting on the body, [tex]\(m\)[/tex] is the mass, and [tex]\(a\)[/tex] is the acceleration of the body. Describe Newton's second law in terms of change in momentum.

A. The sum of all external forces acting on the object is equal to the object's change in momentum.
B. The sum of all external forces acting on the object is equal to the rate of change in the momentum of the object.
C. The external force acting on the object is equal to the object's impulse.
D. The external force acting on the object is equal to the inverse of the object's impulse.

Sagot :

GinnyAnswer
Newton's second law of motion can be expressed in terms of momentum. To understand this, let's recall that momentum ([tex]\( p \)[/tex]) is defined as the product of mass ([tex]\( m \)[/tex]) and velocity ([tex]\( v \)[/tex]):
[tex]\[ p = mv \][/tex]

Newton's second law states that the sum of all external forces ([tex]\( \sum F \)[/tex]) acting on a body is equal to the mass ([tex]\( m \)[/tex]) of the body times its acceleration ([tex]\( a \)[/tex]):
[tex]\[ \sum F = ma \][/tex]

Acceleration ([tex]\( a \)[/tex]) can be expressed as the rate of change of velocity over time ([tex]\( t \)[/tex]):
[tex]\[ a = \frac{dv}{dt} \][/tex]

Substituting this expression for acceleration in Newton's second law gives:
[tex]\[ \sum F = m \frac{dv}{dt} \][/tex]

Rewriting this, we get:
[tex]\[ \sum F = \frac{d(mv)}{dt} \][/tex]

Since [tex]\( mv \)[/tex] is momentum ([tex]\( p \)[/tex]), the equation becomes:
[tex]\[ \sum F = \frac{dp}{dt} \][/tex]

This means that the sum of all external forces ([tex]\( \sum F \)[/tex]) acting on an object is equal to the rate of change of the object's momentum ([tex]\( \frac{dp}{dt} \)[/tex]).

Hence, the correct description of Newton's second law in terms of change in momentum is:
The sum of all external forces acting on the object is equal to the rate of change in the momentum of the object.
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