Question

the kinetic energy of mass 5kg and momentum of 10kg m/s is​

Answer 1

Given :-

• Mass of object is 5kg
• Momentum of object is 10kg m/s

To Find :-

• The kinetic energy of the object.

Answer :-

Given that mass of the body is 5kg and its momentum is 10kg m/s. So , we know a know a relation between mass , momentum and Kinetic energy as ;

$\boxed{\boxed{\red{\sf Energy_{Kinetic}=\dfrac{p^{2}}{2m}}}}$

⇒ KE = p² / 2m

⇒ KE = ( 10 kg m/s )² / 2* 5kg

⇒ KE = 100 kg²- m² s-² / 10kg

⇒ KE = 10 Joules .

$\Large\boxed{\pink{\sf \red{\checkmark}Kinetic\: Energy=\:10\:Joules}}$

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Derivation of used Formula :-

We know that Momentum (p) = mass*velocity

⇒ p = mv .

⇒ p² = m²v²

⇒ v² = p² /m² ............[i]

Also we know that KE = 1/2 mass*(Velocity)²

⇒ KE = ½ mv²

⇒ KE = ½ m ( p²/m²) [ From (i) ]

⇒ KE = p² * ½ * m²/m

⇒ KE = p²/2m .

$\Large\boxed{\red{\sf \blue{\checkmark}\:And\:we\:are\:done\:!}}$