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A point moves with uniform acceleration ...

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

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)`

Text Solution

Verified by Experts

The correct Answer is:
B
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_2)/(v_2 - v_3) = ((t_1 + t_2))/((t_2 + t_3))`
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