Question

When the speed of a car is $v$, the minimum distance over which it can be stopped is $s$. If the speed becomes $nv$, what will be the minimum distance over which it can be stopped during same retardation

• A. $s/n$
• B. $ns$
• C. $s/n^2$
• D. $n^{2}s$

Answer 1

Answer: (D)

$n^{2}s$

Using, $v{}^2=u{}^2+2as$ or $v{}^2-u{}^2=2as$
Maximum retardation, $a=v{}^2/2s$
When the initial velocity is $nv$, then the distance over which it can be stopped is given by
$s_n=\frac{u_0{}^2}{2a}=\frac{\left(nv\right){}^2}{2\left(v{}^2/2s\right)}=n{}^{2}s$