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Question

A body travelling along a straight line traversed one third of the total distance with a velocity 4 m/s. The remaining part of the distance was covered with a velocity 2 m/s for half the time and with velocity 6 m/s for the other half of time. The mean velocity averaged over the whole time of motion is

A
5 m/s
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B
4 m/s
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C
4.5 m/s
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D
3.5 m/s
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Solution

The correct option is B 4 m/s
Let the total distance travelled by the body =s
Let the time taken to cover first one-third of the total distance =t1
Velocity with which the body travelled first one-third of the total distance =4 m/s
Then,
t1=s/34=s12


Let t be the time taken to travel remaining part of the total distance.

Remaining part of the total distance =ss3=2s3

Given that 2s3 was covered with a velocity 2 m/s for half the time and with velocity 6 m/s for the other half of time

2s3=2×t2+6×t2=4t

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