A bus moving at a speed of24m/s begins to slow at a rate of 3 mis each second. How far does it go before stopping?

Options

A. 96 m
B. 72 m
C. 60 m
D. 48 m

Explanation

To solve the problem of how far the bus travels before it comes to a stop, we can use the equations of motion. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Initial velocity (u) = 24 m/s
- Final velocity (v) = 0 m/s (since the bus stops)
- Acceleration (a) = -3 m/s² (the negative sign indicates deceleration)

### Step 2: Use the appropriate equation of motion
We can use the third equation of motion, which is:
\[ v^2 = u^2 + 2as \]
where:
- \( s \) is the distance traveled.

### Step 3: Substitute the known values into the equation
Substituting the values we have:
\[ 0^2 = (24)^2 + 2 \times (-3) \times s \]

### Step 4: Simplify the equation
This simplifies to:
\[ 0 = 576 - 6s \]

### Step 5: Rearrange the equation to solve for s
Rearranging gives:
\[ 6s = 576 \]
\[ s = \frac{576}{6} \]

### Step 6: Calculate the distance
Now, performing the division:
\[ s = 96 \text{ meters} \]

### Conclusion
The bus travels a distance of **96 meters** before coming to a stop.

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