A particle moving in a straight line covers half the distance with a speed of 3 m/s. The other half of the distance is covered in two equal time intervals with speeds of 4.5 m/s and 7.5 m/s respectively. The average speed (in m/s) of the particle during this motion is

Let the total distance be S. The time taken to travel the first half, i.e., S2is t1=S/23=S6Let t2 be the time taken to cover a distance S1 with speed 4.5 m/s and t3 that to cover distance S2 with speed 7.5 m/s.Then S1=4.5t2 and S2=7.5 t3Now, S1+S2=S2 and t2=t3 (given) Therefore S2=S1+S2        =(4.5+7.5)t2 or t2=S12.∴Total time taken t=t1+t2=S6+S12=S4∴ Average speed = total distance  total time =SS/4                              =4 m/s