A car starts from rest and accelerates uniformly to a speed of `180 kmh^(-1)` in 10 s. The distance covered by the car in the time interval is

Options

A. 200 m
B. 300 m
C. 500 m
D. 250 m

Explanation

To solve the problem step by step, we will follow the principles of kinematics.

### Step 1: Identify the Given Values
- Initial velocity (u) = 0 m/s (since the car starts from rest)
- Final velocity (v) = 180 km/h
- Time (t) = 10 s

### Step 2: Convert Final Velocity to m/s
To convert the final velocity from km/h to m/s, we use the conversion factor:
\[ 1 \text{ km/h} = \frac{5}{18} \text{ m/s} \]
Thus,
\[ v = 180 \text{ km/h} \times \frac{5}{18} = 50 \text{ m/s} \]

### Step 3: Calculate Acceleration
We can find the acceleration (a) using the formula:
\[ a = \frac{v - u}{t} \]
Substituting the known values:
\[ a = \frac{50 \text{ m/s} - 0 \text{ m/s}}{10 \text{ s}} = \frac{50}{10} = 5 \text{ m/s}^2 \]

### Step 4: Use the Second Equation of Motion to Find Distance
The second equation of motion states:
\[ s = ut + \frac{1}{2} a t^2 \]
Substituting the values:
- \( u = 0 \)
- \( a = 5 \text{ m/s}^2 \)
- \( t = 10 \text{ s} \)

So,
\[ s = (0 \times 10) + \frac{1}{2} \times 5 \times (10)^2 \]
\[ s = 0 + \frac{1}{2} \times 5 \times 100 \]
\[ s = \frac{5 \times 100}{2} \]
\[ s = \frac{500}{2} = 250 \text{ m} \]

### Final Answer
The distance covered by the car in the time interval is **250 meters**.

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