Question

A person traveling on a straight line moves with a uniform velocity v1 for a distance x and with a uniform velocity v2 for the next equal distance. The average velocity v is given by

(a) v=(v1+v2)

(b) v=√(v1v2)

(c) 2/v=1/v1+1/v2

(d) 1/v=1/v1+1/v2

Answer 1

(c) 2/v = 1/v1 + 1/v2.

Explanation:

Time taken during first phase = x/v1 and during second phase = x/v2.

Total distance =2x

Total time taken = (x/v1)+(x/v2) = x(1/v1 +1/v2)

Average velocity =Total distance/Total time taken

v = 2x / x(1/v1 +1/v2)

=>v = 2/(1/v1 +1/v2)

=> 2/v = (1/v1 +1/v2) {Multiplying both sides by (1/v1 +1/v2)/v }