Question

A person travelled from A to B with force V1 of then B to A awith speed V2 find the average speed
​

Answer 1

Answer:

$\boxed{\bf average \ speed=\frac{2V_1V_2}{V_1+V_2}}$

Explanation:

$\text{Let the distance from A to B be \bf S} \\\\ \text{A person travelled from A to B with speed} \ V_1 \\ \text{and then from B to A with speed }V_2 \\\\ \text{time taken to travel from A to B,}t_1 = \frac{S}{V_1} \\ \text{time taken to travel from B to A,}t_2=\frac{S}{V_2} \\\\ \boxed{\bf average \ speed = \frac{total \ distance}{total \ time}} \\\\ = \frac{S+S}{t_1+t_2} \\\\ =\frac{2S}{\frac{S}{V_1}+\frac{S}{V_2} } \\\\=\frac{2S}{S(\frac{1}{V_1}+\frac{1}{V_2})}$

$=\frac{2}{\frac{1}{V_1}+\frac{1}{V_2}} \\\\=\frac{2}{\frac{V_1+V_2}{V_1V_2}}\\\\ \boxed{\bf average \ speed=\frac{2V_1V_2}{V_1+V_2}}$