A) \[72\]
B) \[92.5\]
C) \[102.6\]
D) \[129.6\]
Correct Answer: D
Solution :
Key Idea: 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\[s=129.6\,\,m\]
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