A bus 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, evaluate.
(a)the maximum velocity achieved and (b)the total distance travelled graphically.

Explanation

To solve the problem step by step, we will analyze the motion of the bus during its acceleration and deceleration phases.

### Step 1: Identify the phases of motion
The bus undergoes two phases:
1. **Acceleration Phase**: The bus accelerates from rest with a constant acceleration \( \alpha \) for a time \( t_1 \).
2. **Deceleration Phase**: The bus then decelerates with a constant deceleration \( \beta \) for a time \( t_2 \) until it comes to rest.

### Step 2: Relate the times
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