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
(a) $v=\frac{v_1+v_2}{2}$
(b) $v=\sqrt{v_1{v}_2}$
(c) $\frac{2}{v}=\frac{1}{v_1}+\frac{1}{v_2}$
(d) $\frac{1}{v}=\frac{1}{v_1}+\frac{1}{v_2}$

Answer 1

(a) $v=\frac{v_1+v_2}{2}$

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, $t=t+t=2t$
$\therefore$ Average velocity, $v=\frac{d_1+d_2}{2t}=\frac{v_1+v_2}{2}$