A bus moving along a straight highway with a speed of 72 km `h^(-1)` is brought to rest within a distance of 50 m. How long does it take for the bus to stop?

Answer

To solve the problem of how long it takes for a bus moving at 72 km/h to come to a stop over a distance of 50 meters, we can follow these steps:

### Step 1: Convert the speed from km/h to m/s
The initial speed of the bus is given as 72 km/h. We need to convert this speed into meters per second (m/s) using the conversion factor:
\[ 1 \text{ km/h} = \frac{5}{18} \text{ m/s} \]
Thus,
\[ \text{Initial speed (U)} = 72 \times \frac{5}{18} = 20 \text{ m/s} \]

### Step 2: Identify the known values
- Initial velocity (U) = 20 m/s
- Final velocity (V) = 0 m/s (since the bus comes to rest)
- Distance (S) = 50 m

### Step 3: Use the third equation of motion to find acceleration
We can use the third equation of motion:
\[ V^2 = U^2 + 2aS \]
Substituting the known values:
\[ 0 = (20)^2 + 2a(50) \]
This simplifies to:
\[ 0 = 400 + 100a \]
Rearranging gives:
\[ 100a = -400 \implies a = -4 \text{ m/s}^2 \]
(The negative sign indicates deceleration or retardation.)

### Step 4: Use the first equation of motion to find time
Now we can use the first equation of motion:
\[ V = U + at \]
Substituting the known values:
\[ 0 = 20 + (-4)t \]
Rearranging gives:
\[ 4t = 20 \implies t = \frac{20}{4} = 5 \text{ seconds} \]

### Conclusion
The time taken for the bus to stop is **5 seconds**.

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