Question

A body is moving with a velocity $1m{s}^{-1}$ a force $F$ is needed to stop it within a distance $x$. If the speed of the body is $3m{s}^{-1}$, the force needed to stop it with in the same distance ($x$) will be:

• A. $9F$
• B. $6F$
• C. $3F$
• D. $1.5F$

Answer 1

Answer: (A)

$9F$

Work done by force $Fx=\frac{1}{2}m{v}^2$ Given $v=1m/s$
$\Rightarrow Fx=\frac{1}{2}m$
Now, suppose force needed to stop the same body moving at $3m/s$, is $f$.

Using force energy theorem:

$\Rightarrow fx=\frac{1}{2}9m$
$\Rightarrow f=9F$