Question

A person travelling on a straight line moves with a uniform velocity v₁ for some time and with uniform velocity v₂ for the next equal time. The average velocity v is given by

Options

• \[v = \frac{v_1 + v_2}{2}\]
• \[v = \sqrt{v_1 v_2}\]
• \[\frac{2}{v} = \frac{1}{v_1} + \frac{1}{v_2}\]
• \[\frac{1}{v} = \frac{1}{v_1} + \frac{1}{v_2}\]

Answer 1

\[v = \frac{v_1 + v_2}{2}\]

Velocity is uniform in both cases; that is, acceleration is zero.
We have: \[d_1 = v_1 t\]  and \[d_2 = v_2 t\]

Total displacement, \[d = d_1 + d_2\]
Total time, \[t = t + t = 2t\]

∴  Average velocity,

\[v = \frac{d_1 + d_2}{2t} = \frac{v_1 + v_2}{2}\].