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 (a) the maximum velocity reached and (b) the total distance travelled.

Options

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

Answer

C

Explanation

`(v_(m))/(t_(1)) = tan theta_(1) = alpha`
`(v_(m))/(t_(2)) = tan theta_(2) = beta`
`:. T_(1) + t_(2) = t ((alpha + beta))/(alpha beta) v_(m)`
`rArr v_(m) = (alpha beta)/(alpha + beta) t`