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

1 Answer
A08
Aug 21, 2017

This is what I get

Explanation:

Let #bar(AB)# be the distance between the given points.

Time taken for movement from #Ato B# #="Distance"/"Velocity"=bar(AB)/u#
Time taken for movement from #Bto A# #=bar(AB)/v#

Time taken for the whole journey#=bar(AB)/u+bar(AB)/v=bar(AB)((v+u)/(uv))#

Distance travelled during whole journey#=bar(AB)+bar(AB)=2bar(AB)#

Average speed of the whole journey#="Total distance"/"Total time"#
#=># Average speed #=(2bar(AB))/(bar(AB)((v+u)/(uv)))#
#=># Average speed #=(2uv)/(v+u#

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