A racing car travels on a track ABCDEFA. ABC is a circular arc of radius 2 R. CD and FA are straight paths of length R and DEF is a circular arc of radius R = 100 m. The coefficient of friction on the road is μ = 0.1. The maximum speed of the car is 50 m/s. Find the minimum time for completing one round.
A racing car travels on a track ABCDEFA. ABC is a circular arc of radius 2 R. CD and FA are straight paths of length R and DEF is a circular arc of radius R = 100 m. The coefficient of friction on the road is μ = 0.1. The maximum speed of the car is 50 m/s. Find the minimum time for completing one round.

Time taken from A to B to C
\mathrm{S} 1= length \mathrm{pf} path =3 / 42 \pi(2 \mathrm{R})=300 \pi \mathrm{m}
\mathrm{V} 1= speed(maximum) along the circular path of the car
\begin{array}{l} =\sqrt{\pi r g}=\sqrt{(0.1)(2 R)(g)} \\ {=14.14 \mathrm{~m} / \mathrm{s}} \\ {\mathrm{T} 1=\mathrm{S} 1 / \mathrm{V} 1=66.62 \mathrm{sec}} \end{array}
Time: C to D and F to A
\mathrm{V} 2 is the maximum speed =50 \mathrm{~m} / \mathrm{s}
\mathrm{T} 2=\mathrm{S} 2 / \mathrm{V} 2=4 \mathrm{sec}
Time : D to E to F
\begin{array}{l} S 3=1 / 42 \pi R=50 \pi \\ V 3=\sqrt{\mu r g}=\sqrt{(0.1)(100)(10)=10 \mathrm{~m} / \mathrm{s}} \\ \mathrm{T} 3=\mathrm{S} 3 / \mathrm{V} 3=15.70 \mathrm{sec} \end{array}
Hence, total time taken by the car =\mathrm{T} 1+\mathrm{T} 2+\mathrm{T} 3=86.32 \mathrm{sec}