Answer:
Explanation:
From A to B
distance traveled with velocity [tex] v_1[/tex] in time [tex]t_1[/tex]
[tex]\frac{d}{2}=v_1t_1----1[/tex]
from B to C
distance traveled is 0.5 d with [tex]v_2[/tex] and [tex]v_3[/tex] velocity for half-half time
[tex]\frac{d}{2}=\frac{v_2t_2}{2}+\frac{v_3t_3}{2}----2[/tex]
divide 1 and 2 we get
[tex]\frac{1}{1}=\frac{2v_1t_1}{v_2t_2+v_3t_3}[/tex]
[tex]\frac{t_1}{t_2}=\frac{v_2+v_3}{2v_1}[/tex]
Now average velocity is given by
[tex]v_{avg}=\frac{d}{t_1+t_2}[/tex]
taking [tex]t_1[/tex] common
[tex]v_{avg}=\frac{2v_1t_1}{t_1(1+\frac{t_2}{t_1})}[/tex]
[tex]v_{avg}=\frac{2v_1}{1+\frac{2v_1}{v_2+v_3}}[/tex]
[tex]v_{avg}=\frac{2v_1(v_2+v_3)}{2v_1+v_2+v_3}[/tex]
