Question

A bus travels for a certain time. it's speed during the first half time is v1 and that during the second half time is v2. the average speed during the whole journey is

Answer 1

Use distance /time formula u will get the answer

Answer 2

Question: A bus travels for a certain time. it's speed during the first half time is $v_1$ and that during the second half time is $v_2$. What is the average speed during the whole journey?

Solution: Let the total time be $2t$. Then the distance covered during the first half $t$ is,

$x_1=v_1t$

And during the second half time is,

$x_2=v_2t$

Average speed    $v_a_v=\frac{x_1+x_2}{2t} = \frac{v_1+v_2}{2}$

Thus, the average speed is the arithmetic mean of the two speeds.

→ Points to Note: The above problem may be generalized as follows:

If the car travels distances, $x_1$, $x_2$, ...,$x_n$ for time intervals $t_1$, $t_2$, ...,$t_n$, respectively, then

$v_a_v=\frac{x_1+x_2+ ...+x_n}{t_1+t_2+...+t_n}$

$= \frac{v_1t_1+v_2t_2+...+v_nt_n}{t_1+t_2+...+t_n}$

If, $t_1=t_2=...= t_n=t,$ then

$v_a_v=\frac{v_1+v_2+...+v_n}{n}$