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

Answer

D

Explanation

Let the car accelerate at rate `alpha` for time `t_1` then maximum velocity attained, `v = 0 + alpha t_1 = alpha t_1`
Now, the car decelerates at a rate `beta` for time `(t - t_1)` and finally comes to rest. Then,
`0 = v - beta(t - t_1) rArr 0 = alpha t_1 - beta t + beta t_1`
`rArr t_1 = (beta)/(alpha + beta) t`
`:. v = (alpha beta)/(alpha + beta)t`.