A train moving with a velocity of 20 m `s^(-1)`' is brought to rest by applying brakes in 5 s. Calculate the retardation.

Explanation

To solve the problem of calculating the retardation of the train, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Initial velocity (u) = 20 m/s (the velocity of the train before braking)
- Final velocity (v) = 0 m/s (the train comes to rest)
- Time (t) = 5 s (the duration over which the brakes are applied)

2. **Use the Equation of Motion:**
We can use the equation of motion that relates initial velocity, final velocity, acceleration (or retardation), and time:
\[ v = u + at \]
where:
- \( v \) = final velocity
- \( u \) = initial velocity
- \( a \) = acceleration (which will be negative in this case since it is retardation)
- \( t \) = time

3. **Substitute the Known Values:**
Plugging in the values we have:
\[ 0 = 20 + a \cdot 5 \]

4. **Rearranging the Equation:**
To find the acceleration (a), rearrange the equation:
\[ a \cdot 5 = 0 - 20 \]
\[ a \cdot 5 = -20 \]

5. **Solve for Acceleration (a):**
Now, divide both sides by 5 to isolate \( a \):
\[ a = \frac{-20}{5} = -4 \, \text{m/s}^2 \]

6. **Identify Retardation:**
Since acceleration is negative, it indicates retardation. Therefore, the retardation is:
\[ \text{Retardation} = 4 \, \text{m/s}^2 \]

### Final Answer:
The retardation of the train is \( 4 \, \text{m/s}^2 \).

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