**Retardation Produced by the Truck's Brakes:**

To calculate the retardation produced by the truck's brakes, we can use the equation of motion:

v^2 = u^2 + 2as

Where:
v = final velocity (54 km/h)
u = initial velocity (90 km/h)
a = retardation (to be determined)
s = distance (20 m)

First, we need to convert the velocities from km/h to m/s:
1 km/h = (1000 m)/(3600 s) = 5/18 m/s

So, the initial velocity (u) is:
u = 90 km/h * (5/18) m/s = 25 m/s

The final velocity (v) is:
v = 54 km/h * (5/18) m/s = 15 m/s

Now, we can substitute the values into the equation of motion and solve for a:
15^2 = 25^2 + 2a(20)
225 = 625 + 40a
40a = -400
a = -10 m/s^2

Therefore, the retardation produced by the truck's brakes is -10 m/s^2. The negative sign indicates that the truck is decelerating.

**Time for Which the Brakes are Applied:**

To calculate the time for which the brakes are applied, we can use the equation of motion:

v = u + at

Where:
v = final velocity (54 km/h)
u = initial velocity (90 km/h)
a = retardation (-10 m/s^2)
t = time (to be determined)

First, let's convert the velocities from km/h to m/s:
u = 90 km/h * (5/18) m/s = 25 m/s
v = 54 km/h * (5/18) m/s = 15 m/s

Now, we can substitute the values into the equation of motion and solve for t:
15 = 25 + (-10)t
10t = 10
t = 1 s

Therefore, the brakes are applied for 1 second.

**Explanation:**

When the truck is running at 90 km/h, it starts to slow down due to the application of its brakes. The truck's initial velocity is 90 km/h, which is converted to 25 m/s. The final velocity is 54 km/h, converted to 15 m/s. The distance over which the truck slows down is given as 20 m.

Using the equation of motion, we can determine the retardation produced by the truck's brakes. Substituting the known values into the equation, we find that the retardation is -10 m/s^2. The negative sign indicates that the truck is decelerating.

To calculate the time for which the brakes are applied, we use another equation of motion. By substituting the initial and final velocities, as well as the retardation, we find that the brakes are applied for 1 second.

In summary, the truck's brakes produce a retardation of -10 m/s^2, and they are applied for 1 second over a distance of 20 m, resulting in the truck slowing down from 90 km/h to 54 km/h.