Question

A particle falling from rest under gravity covers a distance $x$ in $4s$. If it continues falling then next $2x$ distance will be covered in approximately

• A. $1.41s$
• B. $1.73s$
• C. $2.05s$
• D. $2.92s$

Answer 1

The correct option is D $2.92s$

$h=\frac{1}{2}g{t}^2$

given $x=\frac{1}{2}g(4{)}^2=89$ ....(1)

Next 2x means total x+2x=3x from rest

so just use $h=\frac{1}{2}g{t}^2$

& put h = 3x

we get $3x=\frac{g{t}^2}{2}$

$\Rightarrow t^2=\frac{6x}{9}$

$\Rightarrow t=\sqrt{\frac{6x}{9}}=\sqrt{\frac{6}{9}\times 89}$ ; from equation

$\Rightarrow t=\sqrt{48}=4\sqrt{3}=4\times 1.732=6.928sec$

So time for distance b/w x & 3x

will be 6.928 - 4 = 2.928 sec