A particle travels first half of the total distance with speed `v_1.` In second half distace with speed in1/3 rd timeis `v_2.` and in remaining 2/3 rd time constant speed is `v_3.` Find the average speed during the complete journey.

Answer

A, B, C

Explanation

`CD+DB=d rArr v_2(t/3)+((2t)/3)(v_3)=d`
or `t=(3d)/(v_2+2v_3)…….(i)`
Further, `t_(AC)=d/v_1`
Now, Average speed `= ("total distance")/("total time") =(d+d)/(t_(AC)+t_(CD)+t_(DB))`
`=(2d)/(d/v_1+t/3+(2t)/3)=(2d)/((d/v_1+t))`
substituting value of t from Eq.(i), we have
average speed `= (2d)/((d/v_1)+(3d/v_2+2v_3))`
`=(2v_1(v_2+2v_3))/(3v_1+v_2+2v_3)`