A person travelling at 43.2 km/h applies the brake giving a deceleration of `6.0 m/ss^2` to his scooter. How far will it travel before stopping?

Explanation

To solve the problem of how far the scooter will travel before stopping, we can follow these steps:

### Step 1: Convert the speed from km/h to m/s
The initial speed of the scooter is given as 43.2 km/h. To convert this to meters per second (m/s), we use the conversion factor:

\[ \text{Speed in m/s} = \text{Speed in km/h} \times \frac{5}{18} \]

Calculating this gives:

\[ \text{Speed in m/s} = 43.2 \times \frac{5}{18} = 12 \, \text{m/s} \]

### Step 2: Identify the known values
Now we have:
- Initial velocity \( u = 12 \, \text{m/s} \)
- Final velocity \( v = 0 \, \text{m/s} \) (since the scooter stops)
- Deceleration \( a = -6.0 \, \text{m/s}^2 \) (negative because it is a deceleration)

### Step 3: Use the kinematic equation
We will use the third equation of motion, which relates initial velocity, final velocity, acceleration, and displacement:

\[ v^2 = u^2 + 2as \]

Rearranging this to solve for displacement \( s \) (which we will denote as \( d \)) gives:

\[ d = \frac{v^2 - u^2}{2a} \]

### Step 4: Substitute the known values
Substituting the known values into the equation:

\[ d = \frac{0^2 - (12)^2}{2 \times (-6)} \]

This simplifies to:

\[ d = \frac{-144}{-12} = 12 \, \text{m} \]

### Conclusion
The distance the scooter will travel before stopping is \( 12 \, \text{m} \).

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