Two bodies move in a straight line towards each other at initial velocities v1 and v2 and with constant acceleration a1 and a2 directed against the corresponding velocities at the initial instant. The maximum initial separation lmax between the bodies for which they will meet during the motion is:

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Two bodies move in a straight line towards each other at initial velocities v₁ and v₂ and with constant acceleration $a_{1}$ and a₂ directed against the corresponding velocities at the initial instant. The maximum initial separation l_maxbetween the bodies for which they will meet during the motion is:

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$\frac{v_{1}^{2}}{a_{1}} + \frac{v_{2}^{2}}{a_{2}}$

$\frac{{(v_{1} + v_{2})}^{2}}{2 (a_{1} + a_{2})}$

$\frac{v_{1} v_{2}}{\sqrt{a_{1} a_{2}}}$

$\frac{(v_{1}^{2} + v_{2}^{2})}{(a_{1} - a_{2})}$

answer is B.

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Detailed Solution

Relative velocity = v₁ + v₂,Relative acceleration = - (a₁+ a₂)
Now by using $v^{2}$ = $u^{2}$ + 2as,we have
0² = (v₁ + v₂)² - 2 (a₁ + a₂) I_max
I_max = $\frac{{(v_{1} + v_{2})}^{2}}{2 (a_{1} + a_{2})}$