Question

b)Derive an expression for kinetic energy of an object of mass 'm' moving with velocity 'v'​

Answer 1

Answer:

$\frac{1}{2}$m$v^{2}$

Explanation:

Answer 2

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Kinetic energy is the energy of a body due to it's motion.

Derivation :-

suppose there is a body of mass (M) which is at rest when a force (F)is applied on the body the body undergoes displacement (S) .

Now the work done by force on object is equals to product of force and displacement.

W = F × S ------(1)

Now the magnitude of displacement can be calculated by third equation of motion:

${v}^{2} = {u}^{2} + 2as$

$s = \frac{ {v}^{2} - {u}^{2} }{2a}$

And the magnitude of force is equals to the product of mass and acceleration of body.

Now we get :

S = V^2 - U^2 /2a

F = m × a

After inputting the known values in first equation we get :

$w = m \times a( \frac{ {v}^{2} - {u}^{2} }{2a} )$

Since the body was initially at rest does the initial velocity of body is 0m/s

$w = \frac{m \times {v}^{2} }{2}$

This equation can be represented by :

$w = \frac{1}{2} \times m {v}^{2}$

Thus the work done by the force on body is half of product of its mass and square of velocity.

Hence Derived...

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BY SCIVIBHANSHU

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