Calculating acceleration:
To calculate acceleration, we can use the formula:

acceleration = (final velocity - initial velocity) / time

In this case, the initial velocity is 36 km/h, the final velocity is 70 km/h, and the time is 5 seconds. Converting the velocities to meters per second (m/s) and the time to seconds (s), we get:

initial velocity = 36 km/h = 10 m/s
final velocity = 70 km/h = 19.4 m/s
time = 5 s

Using the formula, we get:

acceleration = (19.4 m/s - 10 m/s) / 5 s
acceleration = 1.88 m/s^2

Therefore, the acceleration of the car is 1.88 m/s^2.

Calculating retardation:
Retardation is the opposite of acceleration and refers to the rate at which an object slows down. In this case, the car stops in 20 seconds, so we need to calculate the retardation.

We can use the same formula as before, but this time the final velocity is 0 m/s (since the car stops) and the initial velocity is 70 km/h (which we need to convert to m/s):

initial velocity = 70 km/h = 19.4 m/s
final velocity = 0 m/s
time = 20 s

Using the formula, we get:

retardation = (0 m/s - 19.4 m/s) / 20 s
retardation = -0.97 m/s^2

The negative sign indicates that the car is slowing down, or decelerating. Therefore, the retardation of the car is 0.97 m/s^2.

Explanation:
Acceleration and retardation are both examples of changes in velocity, which is a vector quantity that includes both speed and direction. Acceleration refers to an increase in velocity (either in speed, direction, or both), while retardation refers to a decrease in velocity.

In both cases, we use the formula:

change in velocity = (final velocity - initial velocity)

And then divide by the time it takes to make that change. This gives us the rate at which the velocity is changing, or the acceleration/retardation.

In the case of the car speeding up, the rate of change in velocity is positive (since the velocity is increasing), so we have a positive acceleration. In the case of the car stopping, the rate of change in velocity is negative (since the velocity is decreasing), so we have a negative retardation.

Overall, acceleration and retardation are important concepts in physics and are used to describe a wide range of phenomena, from the motion of cars to the behavior of subatomic particles.