Question

A person is traveling on a straight road with a uniform velocity $v_1$ for some time and with uniform velocity $v_2$ for next equal time. The average velocity for the entire trip is

• A. $\frac{2v_1+v_2}{2}$
• B. $\frac{2v_1{v}_2}{v_1+v_2}$
• C. $\frac{v_1+2v_2}{2}$
• D. $\frac{v_1+v_2}{2}$

Answer 1

The correct option is D $\frac{v_1+v_2}{2}$

Consider a person travelling with uniform velocity $v_1$ for time t.
∴ Displacement of person, $s_1=Velocity\times Time=v_{1}t$
For the next equal time t, the person travels with velocity $v_2$.
Now, displacement of person, $s_2=Velocity\times Time=v_{2}t$
$\text{Average velocity:}=\frac{\text{Total displacement}}{\text{Total time taken}}$
$\Rightarrow v_{av}=\frac{s_1+s_2}{t+t}$
$\Rightarrow v_{av}=\frac{v_{1}t+v_{2}t}{2t}$
$\Rightarrow v_{av}=\frac{v_1+v_2}{2}$
Hence, the correct answer is option (d).