Mathematical formulation of second law of motion class 9


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Mathematical formulation of second law of motion

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Suppose

m= mass of the object

u=initial velocity of the object

v=final velocity of the object

a=uniform acceleration

t=time taken in acceleration

F=constant force

Let the initial and final momentum be p1=mu and p2=mv respectively .

The change in momentum =p2-p1

=mv-mu

=m(v-u)

The rate of change of momentum

=m(v-u)/t

According to 2nd law of motion

F=m(v-u)/t

F=ma [since a=(v-u)/t]

Therefore second law of motion gives us a method to measure the force acting on an object as the product of its mass and acceleration.

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