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.
