Question

A particle moves from A to B with constant velocity u and comes back with constant velocity v. Derive the formula of average speed of the whole journey

Answer 1

LET DISTANCE BETWEEN 'A' AND 'B' BE x

A---→B
Velocity : u
Distance : x
Time taken= Distance/Speed
= x/u
B---→A
Velocity : v
Distance: x
Time taken = Distance/Speed
= x/v

Total distance covered : x+x=2x
Total time taken= x/u + x/v
→ x(v + u)/uv

Average Speed
= Distance/Total time
= 2x/[x(v+u)/uv]
= 2uv/(v+u)

Average Speed is 2uv/(v+u)

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