Average speed is defined as the total path length travelled divided by the total time interval during which the motion has taken place .

1. Identify Parameters: Let the total distance be $d$. Distance covered in the first half = $d/2$ with speed $v_1$.

• Distance covered in the second half = $d/2$ with speed $v_2$.

2. Calculate Time Taken: Time for the first half, $t_1 = \frac{\text{Distance}}{\text{Speed}} = \frac{d/2}{v_1} = \frac{d}{2v_1}$. Time for the second half, $t_2 = \frac{d/2}{v_2} = \frac{d}{2v_2}$.

• Total time, $T = t_1 + t_2 = \frac{d}{2v_1} + \frac{d}{2v_2} = \frac{d}{2} \left( \frac{1}{v_1} + \frac{1}{v_2} \right) = \frac{d}{2} \left( \frac{v_1 + v_2}{v_1 v_2} \right)$.

3. Calculate Average Speed ($v_{avg}$): $v_{avg} = \frac{\text{Total Distance}}{\text{Total Time}}$ $v_{avg} = \frac{d}{\frac{d(v_1 + v_2)}{2v_1 v_2}}$ $v_{avg} = \frac{2v_1 v_2}{v_1 + v_2}$ This result represents the harmonic mean of the individual speeds when equal distances are covered.