A racing car has a uniform acceleration of `4 m//s^(2)`. What distance will it cover in `10 s` after start ?

Options

A. 200 m
B. 500 m
C. 900 m
D. 400 m

Explanation

To solve the problem of how far a racing car with a uniform acceleration of \(4 \, \text{m/s}^2\) will travel in \(10 \, \text{s}\) after starting, we can use the second equation of motion. Here’s a step-by-step solution:

### Step 1: Identify the known values
- Initial velocity (\(u\)) = \(0 \, \text{m/s}\) (since the car starts from rest)
- Acceleration (\(a\)) = \(4 \, \text{m/s}^2\)
- Time (\(t\)) = \(10 \, \text{s}\)

### Step 2: Write down the second equation of motion
The second equation of motion is given by:
\[ S = ut + \frac{1}{2} a t^2 \]
where:
- \(S\) is the distance covered,
- \(u\) is the initial velocity,
- \(a\) is the acceleration,
- \(t\) is the time.

### Step 3: Substitute the known values into the equation
Since the initial velocity \(u = 0\):
\[ S = 0 \cdot t + \frac{1}{2} a t^2 \]
This simplifies to:
\[ S = \frac{1}{2} a t^2 \]

Now, substituting the values of \(a\) and \(t\):
\[ S = \frac{1}{2} \cdot 4 \, \text{m/s}^2 \cdot (10 \, \text{s})^2 \]

### Step 4: Calculate \(t^2\)
Calculating \(t^2\):
\[ (10 \, \text{s})^2 = 100 \, \text{s}^2 \]

### Step 5: Substitute \(t^2\) back into the equation
Now substituting \(t^2\) back into the equation:
\[ S = \frac{1}{2} \cdot 4 \cdot 100 \]

### Step 6: Perform the multiplication
Calculating the right side:
\[ S = 2 \cdot 100 = 200 \, \text{m} \]

### Conclusion
The distance covered by the racing car in \(10 \, \text{s}\) after starting is:
\[ \boxed{200 \, \text{m}} \]