Question

A boy runs along the straight path half of the distance with a velocity v1 and rest half of the dustance with a velocity v2. show that his average velocity V can be given by relation 2/V = 1/v1+1/ v2​

Answer 1

Answer:

Let the total distance be 2d, hence

The boy covered distance d with speed v1 and distance d with speed v2.

v = s/t

t = s/v

Hence,

t1 = d/v1

t2 = d/v2

Total time

= d/v1 + d/v2

= (dv2 + dv1)/v1v2

= d(v1 + v2)/v1v2

Average velocity

= Total Displacement/Total Time

= 2d/ d(v1 + v2)/v1v2

= (2d x v1v2)/d(v1 + v2) (taking reciprocal)

= 2v1v2/(v1 + v2)

V = 2v1v2/(v1 + v2)

V/2 = v1v2/(v1 + v2)

2/V = (v1 + v2)/v1v2

2/V = v1/v1v2 + v2/v1v2

2/V = 1/v2 + 1/v1

2/V = 1/v1 + 1/v2

Hence proved.