The speed of a car travelling on a straight road is listed below at successive intervals of 1 is :
`{:("Time(s)",0,1,2,3,4),("Speed (m/s)",0,2,4,6,8):}`
Which of the following is/are correct? The car travels
1. with a uniform acceleration of 2 `m//s^(2)`.
2. 16 m in 4 s.
3. with an average speed of 4 m/s.
Select the correct answer using the code given below:

Options

A. 1 , 2 and 3
B. 2 and 3 only
C. 1 and 2 only
D. 1 only

Answer

To solve the problem, we need to analyze the given data and verify each statement regarding the car's motion.

### Given Data:
- **Time (s)**: 0, 1, 2, 3, 4
- **Speed (m/s)**: 0, 2, 4, 6, 8

### Step 1: Calculate the acceleration
Acceleration is defined as the change in velocity over time. We can calculate it using the formula:

\[ a = \frac{\Delta v}{\Delta t} \]

From the data:
- Initial speed \( v_0 = 0 \) m/s at \( t = 0 \) s
- Final speed \( v_f = 8 \) m/s at \( t = 4 \) s

Thus, the change in velocity \( \Delta v = v_f - v_0 = 8 - 0 = 8 \) m/s.

The time interval \( \Delta t = 4 - 0 = 4 \) s.

Now substituting these values into the acceleration formula:

\[ a = \frac{8 \, \text{m/s}}{4 \, \text{s}} = 2 \, \text{m/s}^2 \]

**Conclusion for Statement 1**: The car travels with a uniform acceleration of \( 2 \, \text{m/s}^2 \). **(True)**

### Step 2: Calculate the distance traveled in 4 seconds
To find the distance traveled, we can use the formula for distance when acceleration is constant:

\[ s = v_0 t + \frac{1}{2} a t^2 \]

Where:
- \( v_0 = 0 \) m/s (initial speed)
- \( a = 2 \) m/s² (calculated acceleration)
- \( t = 4 \) s

Substituting the values:

\[ s = 0 \cdot 4 + \frac{1}{2} \cdot 2 \cdot (4)^2 \]
\[ s = 0 + \frac{1}{2} \cdot 2 \cdot 16 \]
\[ s = 16 \, \text{m} \]

**Conclusion for Statement 2**: The car travels 16 m in 4 s. **(True)**

### Step 3: Calculate the average speed
Average speed is defined as the total distance traveled divided by the total time taken:

\[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} \]

From the previous calculation:
- Total distance = 16 m
- Total time = 4 s

Substituting the values:

\[ \text{Average speed} = \frac{16 \, \text{m}}{4 \, \text{s}} = 4 \, \text{m/s} \]

**Conclusion for Statement 3**: The average speed is 4 m/s. **(True)**

### Final Conclusion:
All three statements are correct.

### Answer:
The correct answer is **Option 1** (1st, 2nd, and 3rd statements are correct).

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