A particle moves with constant acceleration a and `v_1 v_2 v_3` . are its average velocities in the three successive intervals`t_1 t_2` and `t_3` is of time. Then which relation out of the following holds good for its motion ?

Options

A. `(v_1 -v_2)/(v_2 -v_3) =(t_1 +t_2)/(t_2+t_3)`
B. `(v_1 -v_2)/(v_2 -v_3) =(t_1 -t_2)/(t_2-t_3)`
C. `(v_1 -v_2)/(v_2 -v_3) =(t_1 -t_1)/(t_2-t_3)`
D. `(v_1 -v_2)/(v_2 -v_3) =(t_1 +t_2)/(t_2-t_3)`

Answer

a

Explanation

Here `v_(1)=(u+u+at_(1))/(2)=u+(at_1)/(2)`
Also `v_(2)((u+at_(1))+[u+a(t_1 +t_2)])/(2)`
`u+(2at_(1))/(2) +(1)/(2)at_(2)`
`:.v_2=u+at_(1)+(1)/(2)at_(2)`
Hence `(v_1 -v_2)/(v_2 -v_3)=(t_1 +t_2)/(t_2 +t_3)`