If a car at rest, accelerates uniformly to a speed of `144 km//h` in `20s`, it covers a distance of

Options

A. `2880m`
B. `1440 m`
C. `400 m`
D. `20m`

Answer

To solve the problem of a car accelerating uniformly from rest to a speed of 144 km/h in 20 seconds, we will follow these steps:

### Step 1: Identify the given values
- Initial velocity (u) = 0 m/s (since the car is at rest)
- Final velocity (v) = 144 km/h
- Time (t) = 20 s

### Step 2: Convert the final velocity from km/h to m/s
To convert km/h to m/s, we use the conversion factor \( \frac{5}{18} \):
\[ v = 144 \, \text{km/h} \times \frac{5}{18} = 40 \, \text{m/s} \]

### Step 3: Use the formula to find acceleration (a)
We can use the equation of motion:
\[ v = u + at \]
Substituting the known values:
\[ 40 = 0 + a \cdot 20 \]
Solving for \( a \):
\[ a = \frac{40}{20} = 2 \, \text{m/s}^2 \]

### Step 4: Use the distance formula to find the distance (s)
We can use the formula:
\[ s = ut + \frac{1}{2} a t^2 \]
Substituting the known values:
\[ s = 0 \cdot 20 + \frac{1}{2} \cdot 2 \cdot (20)^2 \]
Calculating:
\[ s = 0 + \frac{1}{2} \cdot 2 \cdot 400 = 400 \, \text{m} \]

### Final Answer
The distance covered by the car is **400 meters**.

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