Question

A person travels along a straight road for the first t/3 time with a speed v1 and for next 2t/3 time with the speed v2 then the mean speed v is given by?

Answer 1

total distance traveled = S = v1 * t/3 + v2 * 2t/3 = (v1 + 2 v2)*t/3
total duration of time = t

average speed = S/t = (v1 + 2 v2)/3

Answer 2

Answer:

The average velocity is $\bold{\frac{1}{3} \times(V 1+2 V 2)}$

Solution:

The average velocity is the rate of change in total displacement with respect to time.

$\text {Average Velocity}=\frac{\text {Total distance}}{\text {Total time}} \rightarrow(1)$

Total distance S can be found by adding the distance covered with speed V1 and time $\frac{t}{3}$ with the distance covered with speed V2 and time $\frac{2 t}{3}$.

$S=S 1+S 2 \rightarrow(2)$

Here S is the total displacement, S1 is the distance covered with speed V1 and S2 is the distance covered with speed V2.

$\bold{S 1=V e l o c i t y \times t i m e=V 1 \times \frac{t}{3}}$

And

$\bold{S 2=\text {Velocity } \times \text { time }=V 2 \times \frac{2 t}{3}}$

Thus,

$S=\left(V 1 \times \frac{t}{3}\right)+\left(V 2 \times \frac{2 t}{3}\right)=\frac{1}{3}(t V 1+2 t V 2)$

Total time is  

$T=\frac{t}{3}+\frac{2 t}{3}=\frac{3 t}{3}=t$

$\text {Average Velocity}=\frac{\frac{t}{3}(V 1+2 V 2)}{t}=\frac{1}{3} \times(V 1+2 V 2)$

Thus the average velocity is $\frac{1}{3} \times(V 1+2 V 2).$