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. `(alphabetat)/((alpha+beta))`
B. `(alphabetat)/(2(alpha+beta))`
C. `(2alphabetat)/((alpha+beta))`
D. `(4alphabetat)/((alpha+beta))`

Answer

A

Explanation

`A` to `B`: `v=alphat_(1)impliest_(1)=v//alpha`
`B` to `C`: `0=v-betat_(2)impliest_(2)=v//beta`
`t_(1)+t_(2)=t`
`v/alpha+v/beta=timpliesv=(alphabetat)/(alpha+beta)`