A vehicle is accelerating on a straight road. Its velocity at any instant is 30 km `h^(-1)` after 2 s, it is 33.6 km `h^(-1)` and after further 2 s, it is 37.2 km `h^(-1)`. Find the acceleration of vehicle in m` s^(-1)`? Is the acceleration uniform ?

Explanation

To solve the problem, we need to find the acceleration of the vehicle in meters per second squared (m/s²) and determine if the acceleration is uniform. Let's break it down step by step.

### Step 1: Convert velocities from km/h to m/s
1. **Initial velocity (V1)**: 30 km/h
\[ V1 = \frac{30,000 \text{ meters}}{3600 \text{ seconds}} = 8.33 \text{ m/s} \]

2. **Velocity after 2 seconds (V2)**: 33.6 km/h
\[ V2 = \frac{33,600 \text{ meters}}{3600 \text{ seconds}} = 9.33 \text{ m/s} \]

3. **Velocity after another 2 seconds (V3)**: 37.2 km/h
\[ V3 = \frac{37,200 \text{ meters}}{3600 \text{ seconds}} = 10.33 \text{ m/s} \]

### Step 2: Calculate the acceleration between the first and second time intervals
1. **Acceleration (a1)** from V1 to V2:
\[ a1 = \frac{V2 - V1}{\Delta t} = \frac{9.33 \text{ m/s} - 8.33 \text{ m/s}}{2 \text{ s}} = \frac{1.00 \text{ m/s}}{2 \text{ s}} = 0.5 \text{ m/s}^2 \]

### Step 3: Calculate the acceleration between the second and third time intervals
1. **Acceleration (a2)** from V2 to V3:
\[ a2 = \frac{V3 - V2}{\Delta t} = \frac{10.33 \text{ m/s} - 9.33 \text{ m/s}}{2 \text{ s}} = \frac{1.00 \text{ m/s}}{2 \text{ s}} = 0.5 \text{ m/s}^2 \]

### Step 4: Determine if the acceleration is uniform
Since \( a1 = 0.5 \text{ m/s}^2 \) and \( a2 = 0.5 \text{ m/s}^2 \), we can conclude that the acceleration is uniform.

### Final Answer
- The acceleration of the vehicle is \( 0.5 \text{ m/s}^2 \).
- The acceleration is uniform.

---