Question

what is kinetic energy Derive an expression for the kinetic energy of a body of mass M moving at speed V​

Answer 1

Answer:

Definition:

It is the energy possessed by an object by virtue of its motion with respect to a reference frame.

Mathematically it involves the following terms :

1) Mass

2) Velocity

Formulas used:

Let kinetic energy be denoted be "K".

So, K = 1/2 mv²

Work done = force × displacement

=> W = F × r,

where "F" is the force and "r" is the displacement

Derivation:

In order to understand this derivation, you must know "integration" and "work -energy" theorem.

As per work energy theorem, the work done is equal to change in kinetic energy.

So let us assume that work done is causing a SMALL CHANGE IN KINETIC ENERGY.

∆K = W

=> δK = F × δr

Integrating on both sides:

=> ∫ δK = ∫ (F × δr)

=> K = ∫ (m × a × δr)

=> K = ∫ {m × (δv/δt) × δr}

=> K = ∫ {m × (δv) × (δr/δt)}

=> K = m ∫ { (δv) × v}

=> K = m ∫ { v × (δv) }

=> K = m × (v²/2)

=> K = 1/2 mv².

(Hence proved)

Answer 2

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__________________________________

The energy possessed by a body by virtue of its motion is known as kinetic energy.

⇒ A moving car is an example of kinetic energy.

K.E. = 1/2 mv²

Here, "m" is the mass of the body and "v" is the velocity.

_______________________

In order to understand this derivation, you must know "integration" and "work -energy" theorem.

As per work energy theorem, the work done is equal to change in kinetic energy.

_______________________

So let us assume that work done is causing a small change in kinetic energy

small change in kinetic energy∆K = W

→ δK = F × δr

Integrating on both sides:

→∫ δK = ∫ (F × δr)

→ K = ∫ (m × a × δr)

→ K = ∫ {m × (δv/δt) × δr}

→ K = ∫ {m × (δv) × (δr/δt)}

→ K = m ∫ { (δv) × v}

→ K = m ∫ { v × (δv) }

→ K = m × (v²/2)

→ K = 1/2 mv²

____________[Hence proved]