Question

A particle covers half of it's distance with a speed v1 and the rest half distance with speed v2. It's average speed during the complete journey is A) (v1+v2) /2
B) (v1v2) /v1+v2
C) (2v1v2) /v1+v2
D) (v1^2v2^2) /v1^2+v2^2

Answer 1

Answer:

Let total distance be = 2d

Hence, the particle travelled d distance with speed v1 and d distance with speed v2.

v=s/t

t=s/v

For part one of the journey, time = d/v1

For part two of the journey, time = d/v2

Total time

= d/v1 + d/v2

= (dv1 + dv2)/v1v2 (taking LCM)

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

Average speed

= Total distance/Total time

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

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

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

Hence the correct answer is option c.

Hope it helped, feel free to contact me for any doubts.