   Chapter 14.3, Problem 95E

Chapter
Section
Textbook Problem

The kinetic energy of a body with mass m and velocity v is K = 1 2 m v 2 . Show that ∂ K ∂ m ∂ 2 K ∂ v 2 = K

To determine

To show: The kinetic energy K=12mv2 satisfies the given equation Km2Kv2=K .

Explanation

Proof:

The kinetic energy is, K=12mv2 , where m is mass and v is velocity.

The equation Km2Kv2=K is to be proved.

Obtain the value of Km2Kv2 .

Km2Kv2=m(12mv2)2v2(12mv2)=12v2m(m)v[12mv(v2)]=12v2(1)v[12m(2v)]<

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