A car starting from rest accelerates uniformly to acquire a speed 20 km `h^(-1)` in 30 min. The distance travelled by car in this time interval will be :

Explanation

To solve the problem step by step, we will follow the physics concepts related to uniformly accelerated motion.

### Step 1: Identify the given data
- Initial speed (u) = 0 km/h (since the car starts from rest)
- Final speed (v) = 20 km/h
- Time (t) = 30 minutes = 0.5 hours (since we need to convert minutes to hours)

### Step 2: Convert final speed to consistent units
Since we are working with time in hours, we can keep the speed in km/h. Thus, we do not need to convert the final speed.

### Step 3: Use the formula to find acceleration
We will use the formula for final velocity in uniformly accelerated motion:
\[ v = u + at \]
Where:
- v = final velocity
- u = initial velocity
- a = acceleration
- t = time

Substituting the known values:
\[ 20 = 0 + a \times 0.5 \]

Now, solving for acceleration (a):
\[ 20 = 0.5a \]
\[ a = \frac{20}{0.5} = 40 \text{ km/h}^2 \]

### Step 4: Calculate the distance traveled using the distance formula
We will use the formula for distance (s) in uniformly accelerated motion:
\[ s = ut + \frac{1}{2} a t^2 \]
Substituting the known values:
- u = 0 km/h
- a = 40 km/h²
- t = 0.5 hours

Now, substituting into the formula:
\[ s = 0 \times 0.5 + \frac{1}{2} \times 40 \times (0.5)^2 \]
\[ s = 0 + \frac{1}{2} \times 40 \times 0.25 \]
\[ s = 0 + \frac{40}{8} \]
\[ s = 5 \text{ km} \]

### Conclusion
The distance traveled by the car in the time interval of 30 minutes is **5 kilometers**.