Question

An automobile travelling at 50 km/h, can be stopped at a distance of 40 m by applying brakes. If the same automobile is travelling at 90 km/h, all other conditions remaining same and assuming no skidding, the minimum stopping distance in metres is:

• A. 72
• B. 92.5
• C. 102.6
• D. 129.6

Answer 1

Answer: (D)

129.6

Answer 2

When automobile stops, final velocity is zero. From equation of motion
${{v}^{2}}={{u}^{2}}-2as$ where $u$ is initial velocity, a is acceleration and s is displacement.
Given, $u=50\,km/h,\,v=0,s=40\,m$
$\therefore$ $a=\frac{{{u}^{2}}}{2s}=\frac{{{\left( 50\times \frac{5}{18} \right)}^{2}}}{2\times 40},$
when $u'=90\,km/h,\,a=\frac{{{\left( 50\times \frac{5}{18} \right)}^{2}}}{2\times 40},v=0$
$s=\frac{u{{'}^{2}}}{2a}$
$\Rightarrow$ $s=\frac{{{\left( 90\times \frac{5}{18} \right)}^{2}}\times 2\times 40}{2\times {{\left( 50\times \frac{5}{18} \right)}^{2}}}$
In metre $s=129.6\,m$