# A Particle Starts From Rest And Moves With Uniform Acceleration If It Covers A Displacement Of Y2 - X2 In The First 10 Sec And Y2 + X2 In The Next First 10 Sec, Then Y =?

Sol:

From the second equation of motion,

$y^{2} – x^{2} = \frac{1}{2}\; a (10)^{2} \;and \;y^{2} – x^{2} + x^{2} = \frac{1}{2}\;a * (20)^{2}\\y^{2} – x^{2} = 50\;a\; and\; y^{2} = 100a\\x^{2} = 50\;a –[1]\\y^{2} = 100\;a –[2]$

From the above equation [1] and [2], we get:

$y^{2} = 2x^{2}\\ y = \sqrt{2}x$

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