A particle covers half of its journey with a constant speed of 'v' , half of the remaining part of journey with a constant speed of 2v and the rest of the journey with a constant speed of 4v. What is the average speed during the entire journey?
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Answered by
72
Let total journey be x
time with speed v =( (1/2)*x)/v = x/2v
remaining part of journey = (1/2)*x
time with speed 2v =( (1/4)*x)/2v = x/8v
time with speed 4v =((1/4)*x)/4v = x/16v
Average speed = total distance/total time
speed = x/(x/2v+x/8v+x/16v)
Average speed = x/(11x/16v) = 16v/11
time with speed v =( (1/2)*x)/v = x/2v
remaining part of journey = (1/2)*x
time with speed 2v =( (1/4)*x)/2v = x/8v
time with speed 4v =((1/4)*x)/4v = x/16v
Average speed = total distance/total time
speed = x/(x/2v+x/8v+x/16v)
Average speed = x/(11x/16v) = 16v/11
Answered by
33
Let total journey be x
time with speed v =( (1/2)*x)/v = x/2v
remaining part of journey = (1/2)*x
time with speed 2v =( (1/4)*x)/2v = x/8v
time with speed 4v =((1/4)*x)/4v = x/16v
Average speed = total distance/total time
speed = x/(x/2v+x/8v+x/16v)
Average speed = x/(11x/16v) = 16v/11
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