A particle covers half of its total distance with speed v1 and the rest half distance with speed v2. Its average speed during the complete journey is

Let S be the total distance travelled by the particle. Let t1 be the time taken by the particle to cover first half of the distance. Then t1=S/2v1=S2v1 Let t2 be the time taken by the particle to cover remaining half of the distance. Then  t2=S/2v2=S2v2Average speed,vav= Total distance travelled  Total time taken =St1+t2=SS2v1+S2v2=2v1v2v1+v2