Science, asked by kaushal3914, 1 year ago

A body travelling along a straight line traversed one half of the total distance was covered with a velocity v0. The remaining part of the distance was covered with a velocity v1, for half of time and with velocity v2 for the other half of time. Find the mean velocity averaged over the whole time of motion....

Answers

Answered by abhi178
54

solution : Let length of path is x.

half of path is travelled by velocity Vo.

so, time taken to cover distance, t1 = (x/2)/Vo = x/2Vo......(1)

now, reaming distance = x/2, is covered with velocity v1 for half time and v2 for other half time.

let time time to cover the distance x/2 is t

then, distance covered with velocity v1 =v1 × (t/2)

and distance covered with velocity v2. =v2 × (t/2)

so, average velocity of particle for remaining (x/2) distance , V' = (v1 × t/2 + v2 × t/2)/(t/2 + t/2) = (v1 + v2)/2

now, time taken to cover (x/2) distance with velocity (v1 + v2)/2 , t2 = (x/2)/(v1 + v2)/2 = x/(v1 + v2).....(2)

now average velocity for whole time of motion, V = total distance/total time taken

= x/(t1 + t2)

from equations (1) and (2),

= x/[x/2Vo + x/(v1 + v2)]

= 2Vo(v1 + v2)/(2Vo + v1 + v2)

hence, average velocity is \bf{\frac{2v_0(v_1+v_2)}{(2v_0+v_1+v_2)}}

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