**Calculating the Retardation Produced by the Truck's Brakes and the Time for which the Brakes are Applied**

To calculate the retardation produced by the truck's brakes and the time for which the brakes are applied, we need to use the formula for acceleration:

\[a = \frac{{v_f - v_i}}{{t}}\]

where:
- \(a\) is the acceleration (or in this case, the retardation),
- \(v_f\) is the final velocity,
- \(v_i\) is the initial velocity, and
- \(t\) is the time taken.

**Given Data**
- Initial velocity (\(v_i\)) = 20 km/h = 20,000 m/3600 s = 5.56 m/s (converted from km/h to m/s)
- Final velocity (\(v_f\)) = 50 km/h = 50,000 m/3600 s = 13.89 m/s (converted from km/h to m/s)
- Distance (\(d\)) = 20 m

**Calculating Retardation**
To calculate the retardation, we can rearrange the acceleration formula as follows:

\[a = \frac{{v_f - v_i}}{{t}} \Rightarrow a \cdot t = v_f - v_i \Rightarrow a = \frac{{v_f - v_i}}{{t}}\]

Substituting the known values:

\[a = \frac{{13.89 - 5.56}}{{t}}\]

**Calculating Time**
To calculate the time, we need to rearrange the above equation:

\[t = \frac{{v_f - v_i}}{{a}}\]

Substituting the known values:

\[t = \frac{{13.89 - 5.56}}{{a}}\]

**Calculating Retardation**
Using the formula for acceleration:

\[a = \frac{{v_f - v_i}}{{t}} = \frac{{13.89 - 5.56}}{{t}}\]

Substituting the known values:

\[a = \frac{{13.89 - 5.56}}{{t}}\]

Simplifying:

\[a = \frac{{8.33}}{{t}}\]

**Calculating Time**
Using the rearranged equation for time:

\[t = \frac{{v_f - v_i}}{{a}} = \frac{{13.89 - 5.56}}{{a}}\]

Substituting the known values:

\[t = \frac{{13.89 - 5.56}}{{a}}\]

Simplifying:

\[t = \frac{{8.33}}{{a}}\]

Let's calculate the retardation and time using the given data.