Two cars start in a race with velocities `u_(1)` and `u_(2)` and travel in a straight line with acceleration `alpha` and `beta`. If both reach the finish line at the same time, the range of the race is

Options

A. `(2(u_(1)-u_(2)))/((beta-alpha)^2)(u_(1)beta-u_(2)alpha)`
B. `(2(u_(1)-u_(2)))/(beta+alpha)(u_(1)alpha-u_(2)beta)`
C. `((2u_(1)-u_(2))^(2))/((beta-alpha)^(2))`
D. `(2u_(1)u_(2))/(betaalpha)`

Answer

A

Explanation

Range`=` dist. Covered before they meet
`S=t(u_(1)+(1)/(2)alpha t)=t(u_(2)+(1)/(2)beta t)`
Sove for `t` and substitute in the above equation.