A car accelerates from rest at a constant rate `alpha` for some time, after which it decelerates at a constant rate `beta,` to come to rest. If the total time elapsed is t seconds. Then evalute the maximum velocity aquired by the car is

Options

A. ` (alpha beta )/( alpha + beta ) t`
B. ` ( alpha + beta )/( alpha beta ) t`
C. ` ( alpha ^(2) + beta ^(2))/( beta alpha ) `
D. ` (alpha + beta^(2))/( beta alpha ) `

Answer

A

Explanation

` t= (v)/(alpha ) +(v)/(beta) `
` rArr v= ( alpha beta t)/( alpha +beta ) `