Question

Figure shows a particle starting from point A, travelling upto B with a speed $s$, then upto point C with a speed $2s$ and finally upto A with a speed of $3s$. Find its average speed.

• A. $1.2\text{s}$
• B. $1.8\text{s}$
• C. $2.4\text{s}$
• D. $3\text{s}$

Answer 1

The correct option is B $1.8\text{s}$


Angle $\angle AOB={90}^{\circ }=\pi /2$, $\angle BOC={120}^{\circ }=2\pi /3$

$\therefore \angle AOC=2\pi -(\frac{\pi }{2}+\frac{2\pi }{3})=\frac{5\pi }{6}$

$t_1=\frac{AB}{s}=\frac{\frac{\pi }{2}R}{s},t_2=\frac{BC}{2s}=\frac{\frac{2\pi }{3}R}{2s},t_3=\frac{CA}{3s}=\frac{\frac{5\pi R}{6}}{3s}$

$\text{Average Speed =}\frac{2\pi R}{t_1+t_2+t_s}=\frac{2\pi R}{\frac{\pi R}{2s}+\frac{\pi R}{3s}+\frac{5\pi R}{18s}}=\frac{2\times 18s}{20}=1.8s$