Question

A particle starts from rest and moves with uniform acceleration. If covers a displacement of $y^2-x^2$ in the first $10sec$ and $y^2+x^2$ in the next first $10sec$, then

• A. $x=\sqrt{2}y$
• B. $x=3y$
• C. $y=3x$
• D. $y=\sqrt{2}x$

Answer 1

Answer: (D)

$y=\sqrt{2}x$

From second equation of motion, $y^2-x^2=\frac{1}{2}a(10{)}^2$ and $y^2-x^2+y^2+x^2=\frac{1}{2}a\times (20{)}^2$

$y^2-x^2=50a$ and $y^2=100a$

$x^2=50a$ (1) and $y^2=100a$ (2)

From equation 1 and 2,

$y^2=2x^2$

$y=\sqrt{2}x$

Hence Option $\text{D}$ is correct answer.