**Calculating Retardation and Time for Brakes Applied**

To calculate the retardation produced by the brakes of the truck and the time for which the brakes are applied, we can use the formula:

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

Where:
- \(v\) is the final velocity of the truck (54 km/h)
- \(u\) is the initial velocity of the truck (90 km/h)
- \(a\) is the retardation produced by the brakes
- \(s\) is the distance over which the truck slows down (20 m)

**Conversion of Units**

Before using the formula, we need to convert the velocities from km/h to m/s. We know that:

1 km = 1000 m
1 hour = 3600 seconds

Therefore, to convert km/h to m/s, we divide the value by 3.6.

The initial velocity (u) of the truck is 90 km/h, which is equal to 25 m/s. The final velocity (v) is 54 km/h, which is equal to 15 m/s.

**Applying the Formula**

Now, we can substitute the values into the formula:

\[15^2 = 25^2 + 2a(20)\]

Simplifying the equation:

\[225 = 625 + 40a\]

Rearranging the equation:

\[40a = 625 - 225\]
\[40a = 400\]

Dividing both sides by 40:

\[a = \frac{400}{40} = 10 \,m/s^2\]

Therefore, the retardation produced by the brakes of the truck is 10 m/s^2.

**Calculating the Time for which the Brakes are Applied**

To calculate the time for which the brakes are applied, we can use the formula:

\[v = u + at\]

Where:
- \(v\) is the final velocity (15 m/s)
- \(u\) is the initial velocity (25 m/s)
- \(a\) is the retardation (-10 m/s^2, as it is opposing the motion)
- \(t\) is the time for which the brakes are applied

Substituting the values into the formula:

\[15 = 25 + (-10)t\]

Simplifying the equation:

\[-10t = 15 - 25\]
\[-10t = -10\]

Dividing both sides by -10:

\[t = \frac{-10}{-10} = 1 \,second\]

Therefore, the brakes are applied for a time of 1 second.

**Conclusion**

- The retardation produced by the brakes of the truck is 10 m/s^2.
- The brakes are applied for a time of 1 second.