Question

derive the relation between kinetic enargy and momentum?​

Answer 1

Kinetic energy and momentum of a moving body can be mathematically related as follow-

Consider the formula of kinetic energy-

K.E=12mv2
Multiply and divide R.H.S by m

⇒K.E=12mv2×mm =m2v22m =(mv)22m
We know that p=mv. Substituting for mv in the above equation we get-

K.E=p22m
The above equation gives the relation between Kinetic energy and momentum of the object which is under motion.

If the Momentum(p) is constant
K.E∝1m

If Kinetic Energy(K.E) is constant
p∝m‾‾√

If mass(m) is constant
p∝K.E‾‾‾‾√

Hope you have understood the relation between Kinetic energy and momentum of a moving object.

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