A person covers half of his journey at a speed of 40 m/sec and the other half at a speed of 50 m/sec. His average speed during the whole journey is about

Concept:

• Speed: The distance travelled by the body in unit time.
• \(Speed = \frac{{Distance}}{{Time}}\)
• Also, \(Time= \frac{{Distance}}{{Speed}}\)
• Average Speed: Since the body does not always have the same speed, So we use the concept of average speed. It is the ratio of total distance covered to total time taken by the body.
• \(Average\;Speed = \frac{{Total\;Distance}}{{Total\;Time}}\)

Average speed: 

• The total path length traveled divided by the total time interval during which the motion has taken place is called the average speed of the particle.

\(Average\;speed\;\left( {\bar v} \right) = \frac{{total\;path\;length\;\left( S \right)}}{{total\;time\;taken\;\left( t \right)}}\)

Calculation:

Given - Let the total distance between the whole journey is 2x

Time taken in 1^st journey (t₁) = x/40 m and Time taken in 2nd journey (t2) = x/50 m 

• The average speed during the whole journey is 

\(\Rightarrow v_{av}=\frac{2x}{\frac{x}{40}+\frac{x}{50}}=\frac{400}{9}=44.4\, m/s\)