Answer
(a) $3\Delta x$
(b) (III)
Work Step by Step
(a) We know that
$v^2=2a\Delta x$......eq(1)
As given that $v=2v$
$\implies (2v)^2-v^2=2ad$
$\implies 3v^2=2ad$.......eq(2)
dividing eq(2) by eq(1), we obtain:
$\frac{3v^2}{v^2}=\frac{2ad}{2a\Delta x}$
This simplifies to:
$d=3\Delta x$
(b) We know that the correct option is statement (III) -- that $W=F*d$ and work depends on the speed squared.
