A point moves with a uniform acceleration and ` v_1 ,v_2, v_3` denote the average velociies in the three succellive intervals of time `t _1` ,` t_2` and `t_3`. Find the ratio of ( `v_1` - `v_2`) and ( `v_2` - `v_3`).

Options

A. `(t_1-t_2)/(t_2-t_3)`
B. `(t_1-t_2)/(t_2+t_3)`
C. `(t_1+t_2)/(t_2-t_3)`
D. `(t_1+t_2)/(t_2+t_3)`

Answer

D

Explanation

Let u be initial velocity and a be uniform acceleration .

Average velocities in the intervals from 0 to `t_(1) , t_(1) " to " t_(2) and t_(2) " to" t_(3) ` are
`v_(1) =(u+u+at_(1))/2=u+a/2t_(1)" "...(i)`
`v_(2) =(u+at_(1)+u+a(t_(1)+t_2))/2=u+at_(1)+a/2t_(2)" "...(ii)`
`v_(3) =(u+a(t_(1)+t_(2))+u+a(t_(1)+t_(2)+t_3))/2`
`=u+at_(1)+at_(2)+a/2t_(3)" "...(iii)`
Subtract (i) from (ii) , we get, `v_(2)-v_(1) =a/2 (t_(2)+t_(3)) " "...(v)`
Divide (iv) by (v), we get
`(v_2-v_1)/(v_3-v_2)=((t_1+t_2))/((t_2+t_3))" or " (v_1-v_2)/(v_2-v_3)=((t_1+t_2))/((t_2+t_3))`