A point moves with uniform acceleration and `v_(1), v_(2)`, and `v_(3)` denote the average velocities in the three successive intervals of time `t_(1).t_(2)`, and `t_(3)` Which of the following Relations is correct?.

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_2) : (t_1 - t_3)`
D. `(v_1 - v_2) : (v_2 - v_3) = (t_1 - t_2) : (t_2 - t_3)`

Answer

B

Explanation

Let `u_1,u_2,u_3` and `u_4` be velocities at time `t = 0, t_1,(t_1 + t_2)` and `(t_1 + t_2 + t_3)` respectively and acceleration is `a` then `v_1 =(u_1 + u_2)/(2), v_2 =(u_2 + u_3)/(2) and v_3 = (u_3 + u_4)/(2)`
Also `u_2 = u_1 + at_1, u_3 = u_1 + a(t_1 + t_2)`
and `u_4 = u_1 + a(t_1 + t_2 + t_3)`
By solving, we get `(v_1 - v_1)/(v_2 - v_3)=((t_1 + t_2))/((t_2 + t_3))`.