Question

show that k.E=1/2mv2 os dimensionaly correct​

Answer 1

Answer:

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Answer 2

Let there be a object of mass m, at rest . A force F acts on it and increases its velocity to v.

By 3rd equation of motion,

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

${v}^{2} - {0}^{2} = 2as \: \: \: (initially \: at \: rest)$

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

$a = \frac{ {v}^{2} }{2s} ............(i)$

Now,

$f \: = ma$

$f = m \times \frac{ {v}^{2} }{2s} \: \: (from \: eq \: i)$

$f = \frac{m {v}^{2} }{2s} ............(ii)$

Now,

$w = fs$

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

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

But work done is equal to energy,

Therefore,

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

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