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 can follow these calculations:

### Step 1: Understand the given information
- The car starts from rest, which means the initial velocity \( u = 0 \) m/s.
- The final velocity \( v = 180 \) km/h.
- The time \( t = 10 \) seconds.

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

### Step 3: Calculate the acceleration
Using the formula for acceleration \( a \):
\[ a = \frac{v - u}{t} \]
Since \( u = 0 \):
\[ a = \frac{50 \, \text{m/s} - 0}{10 \, \text{s}} = \frac{50}{10} = 5 \, \text{m/s}^2 \]

### Step 4: Calculate the distance covered using the formula
We can use the formula for distance \( s \) when starting from rest:
\[ s = ut + \frac{1}{2} a t^2 \]
Substituting \( u = 0 \):
\[ s = 0 \cdot t + \frac{1}{2} a t^2 = \frac{1}{2} \cdot 5 \, \text{m/s}^2 \cdot (10 \, \text{s})^2 \]
Calculating further:
\[ s = \frac{1}{2} \cdot 5 \cdot 100 = \frac{500}{2} = 250 \, \text{m} \]

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

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