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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