Question

A person travelling 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)/2

(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/v_2.

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  }