Question

A body is moving with a speed of $1$ m/s and a constant force $F$ is needed to stop it in a distance $x$. If the speed of the body is $3$ m/s the force needed to stop it in the same distance $x$ will be :

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

Answer 1

The correct option is D $9F$

$u_1=3m/s;u_2=1m/s;v=0\text{in each case};distance=xm$
we know,
$v^2=u^2+2a_{1}x$
$a_1=\frac{3^2}{2x}=\frac{9}{2x}$
$a_2=\frac{1^2}{2x}=\frac{1}{2x}$
$a_1=9a_2$ and mass is constant
Hence,the force required in latter case is 9 times greater than former case.