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. `(upsilon_(1)-upsilon_(2)):(upsilon_(2)-upsilon_(3))=(t_(1)-t_(2)):(t_(2)+t_(3))`
B. `(upsilon_(1)-upsilon_(2)):(upsilon_(2)-upsilon_(3))=(t_(1)+t_(2)):(t_(2)+t_(3))`
C. `(ipsilon_(1)-upsilon_(2)):(upsilon_(2)-upsilon_(3))=(t_(1)-t_(2)):(t_(1)-t_(3))`
D. `(upsilon_(1)-upsilon_(2)):(upsilon_(2)-upsilon_(2)-upsilon_(3))=(t_(1)-t_(2)):(t_(2)-t_(3))`

Answer

B

Explanation

Average velocity in uniformly accelerated motion is given by,
`upsilon_(av)=(s)/(t)=(ut+(1)/(2)at^(2))/(t)=u+(1)/(2)at`
Now, `upsilon_(1)=u+(1)/(2)at_(1), upsilon_(2)=(u+at_(1))+(1)/(2)at_(2)`
and `upsilon_(3)=u+a(t_(1)+t_(2))+(1)/(2)at_(3)`
`therefore upsilon_(1)-upsilon_(2): upsilon_(2)-upsilon_(3)=(t_(1)+t_(2)):(t_(2)+t_(3))`