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

The Correct Option is D

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 $