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.

Explanation

To solve the problem, we will break it down into two parts: (a) finding the maximum velocity reached by the car, and (b) calculating the total distance traveled by the car.

### Step-by-Step Solution:

**Part (a): Finding the Maximum Velocity Reached**

1. **Understanding the Motion**: The car accelerates from rest at a constant rate `α` for a time `t₀`, reaching a maximum velocity `v₀`. Then, it decelerates at a constant rate `β` for the remaining time `t - t₀` until it comes to rest.

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