Question

Race car A follows path $abcde$ while race car B follows path $12C34$ rack if each car has a constant speed corresponding to a normal acceleration of $8$ $m/s^2$ The tracks $abcde$ and $2C3$ are semicircular track while tracks 1-2 and 3-4 are straight track Point $a$ and point $1$ are the starting point of race and point 4 and point e are finishing point of race and point $4$ and point $e$ are finishing point of the race Choose the correct statements

• A. Car A wins the race with time difference $\frac{14+3}{3}s$
• B. car A wins the race with time difference $\frac{14-3}{3}s$
• C. Car B wins the race with time difference $\frac{14+3}{3}s$
• D. car B wins with the race with time difference $\frac{14-3}{3}s$

Answer 1

Answer: (B)

car A wins the race with time difference $\frac{14-3}{3}s$

$a_n=\frac{V^2}{R}\Rightarrow V=\sqrt{a_{A}R}\Rightarrow V_A=\sqrt{8\times 128}=32m/s$

$V_B=\sqrt{8\times 72}=24m/s$

$1_A=\frac{\pi \times 128}{32}=4\pi \sec =12.56\sec$

$t_B=\frac{\pi \times 72+2\times 56}{24}=3\pi +\frac{14}{3}=9.42+4.67=14.09\sec$

$\Delta t=-\pi +\frac{14}{3}=\frac{14-3\pi }{3}\sec$
car $A$ will win the race