A person travelling on a straight line moves with a uniform velocity 
for a distance 
and with a uniform velocity 
for the next 
distance. The average velocity in this motion is 
. If 
is 
then 
_________ 
.
Text Solution
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To find the average velocity given the motion of a person traveling along a straight line with two different velocities, we start by calculating the average velocity ( 
) using the total distance traveled divided by the total time taken.
The distances and velocities are given as follows:
Distance 
at velocity 
Distance 
at velocity 
The formula for average velocity is:
Given:
The total distance traveled is:
The time taken to cover each segment is given by:
Time for 
Time for 
Now, using the formula for average velocity:
Simplifying the equation:
Cross-multiplying gives:
Solving for 
:
Finally, solving for 
:
Thus, the value of 
is 
.
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