Question

A partide covers each 1/3 of the total distance with speed V1, V2, and V3, respectively. Find the
average speed of the particle​

Answer 1

Answer:

Explanation:

Total distance traveled = S 

Time taken for the 3 parts of the journey = t1, t2 and t3 respectively 

Speed during the 3 parts of the journey = v1, v2, v3, respectively 

Distance covered in part of the journey = S/3 

=> t1 = (S/3)/v1 = S/(3v1) 

t2 = (S/3)/v2 = S/(3v2) 

t3 = (S/3)/v3 = S/(3v3) 

Total time taken = t = t1 + t2 + t3 

= (S/3)(1/v1 + 1/v2 + 1/v3) 

Average speed = V(av) = S/t = S/[(S/3)(1/v1 + 1/v2 + 1/v3)] 

= 1/[(1/3)(1/v1 + 1/v2 + 1/v3)] 

= 1/[(v2 v3 + v3 v1 + v1v2)/{3(v1 v2 v3)}] 

= (3 v1 v2 v3) / (v1 v2 + v2 v3 + v3 v1