A point move with uniform acceleration and `upsilon_(1), upsilon_(2)` and `upsilon_(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_(2)-t_(3))`
D. `(v_(1)-v_(2)):(v_(2)-v_(3))=(t_(1)-t_(2)):(t_(2)-t_(3))`

Answer

B

Explanation

When acceleration is constant the instantaneous velocity is equal to the average velocity in mid of the time interval.
`a=(v_(2)-v_(1))/(t_(1)/2+t_(2)/2)=(v_(3)-v_(2))/(t_(2)/2+t_(3)/2)`