A) 50 m
B) 60 m
C) 40.8 m
D) 80.16 m
Correct Answer: C
Solution :
Key Idea: Frictional force acting between road and lyres retards the motion of automobile. There is a static friction between tyres and road, so frictional force cause the retardation in velocity of a automobile. Free body diagram of automobile is shown. From Newtons third law \[F={{f}_{e}}=\mu R=\mu g\] where m is the mass of automobile. Also, \[F=ma\] \[ma=\mu mg\] \[\Rightarrow \] a = retardation \[=\mu g\] = 0.5 g Let automobile stops at a distance \[x\], then from equation of motion \[{{v}^{2}}={{u}^{2}}-2ax\] Given, \[v=0,u=72\,km/h=72\times \frac{5}{18}m/s\] \[=20\,m/s\] \[g=9.8\,\,m/{{s}^{2}}\] \[\therefore \] \[{{0}^{2}}{{(20)}^{2}}-2\times 0.5\times 9.8\,\,x\] \[\Rightarrow \] \[x=\frac{20\times 20}{2\times 0.5\times 9.8}=40.8\,m\]You need to login to perform this action.
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