Question

THE K.E OF A MOVING BODY IS 250 J
IF THE VELOCITY OF A BODY INCREASED BY 5 TIMES FIND IT NEW K.E​

Answer 1

K.E₁ = 250J

velocity = v

mass = m

K.E₁ = (1/2)mv²

if the velocity is increased by 5times, what is it's new K.E [K.E₂ = ? ]

new velocity = 5v

and mass is unchanged.

mass = m

so,

⇒ K.E₂ = (½) m (5v)²

⇒ K.E₂ = (½)(m)(25v²)

⇒ K.E₂ = (½mv²)(25)

⇒ K.E₂ = 25(250)

⇒ K.E₂ = 6250J

It's New Kinetic Energy is 6250J .

Answer 2

Answer :-

New kinetic energy of the body is 6250 Joules .

Explanation :-

We have :-

→ Kinetic energy of the body = 250 J

→ Increase in velocity (v') = 5 times

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If we consider the first situation, then we get it's equation as :-

⇒ ½mv² = K.E.

⇒ ½mv² = 250 ----(1)

Now, velocity is increased by 5 times i.e. v' = 5v So the equation for new kinetic energy (K.E.') will be :-

⇒ ½m(v')² = K.E.'

⇒ ½m(5v)² = K.E.'

⇒ 25mv² = 2K.E.' ---(2)

On dividing eq(2) by eq(1), we get :-

⇒ 25mv²/(½mv²) = 2K.E.'/250

⇒ 50 = 2K.E.'/250

⇒ 2K.E.' = 12500

⇒ K.E.' = 12500/2

⇒ K.E.' = 6250 J