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A particle starts with an initial veloci...

A particle starts with an initial velocity and passes successively over the two halves of a given distance with constant accelerations `a_1 and a_2` respectively. Show that the final velocity is the same as if the whole distance is covered with a uniform acceleration `(a_1 + a_2)/2 .`

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The correct Answer is:
A


In the first case,
`v_1^2=u^2 + 2a_1 s …(i)`
`v_2^2=v_1^2 + 2a_2 s …(ii)`
Adding Eqs. (i) and (ii), we have
`v_2^2 = u^2 + 2 ((a_1 + a_2)/2) (2s) …(iii)`
In the second case,
`v^2 = u^2 + 2 ((a_1 + a_2)/2) (2s) …(iv)`
From Eqs. (iii) and (iv), we can see that
`v_2=v` Hence Proved.
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