A car approaching a bend in a road has its speed decreased from 30m/s to 10m/s.while traversing. A distance of 30m

Calculate.
1- What's de retardation
2- How long did it take to traverse this distance

To calculate the retardation (rate of deceleration):

1. We can use the formula: retardation = (final velocity - initial velocity) / time

Given:
Initial velocity (u) = 30 m/s
Final velocity (v) = 10 m/s

We need to find the time taken. However, we don't have the time given in the question. So we need to calculate it using the distance traveled and initial/final velocities.

To calculate the time taken:
2. We can use the formula: distance = (initial velocity + final velocity) / 2 * time

Given:
Distance (s) = 30 m
Initial velocity (u) = 30 m/s
Final velocity (v) = 10 m/s

We need to find the time taken.

Let's solve these step by step:

1. Calculating the retardation:
retardation = (final velocity - initial velocity) / time

Since we don't have the time, we will use the distance formula to get the time:
distance = (initial velocity + final velocity) / 2 * time

Rearranging the equation to solve for time:
time = 2 * distance / (initial velocity + final velocity)

Plugging in the given values:
time = 2 * 30 m / (30 m/s + 10 m/s)

Simplifying:
time = 60 m / 40 m/s
time = 1.5 s

Now, with the time calculated, we can find the retardation:
retardation = (final velocity - initial velocity) / time
retardation = (10 m/s - 30 m/s) / 1.5 s
retardation = -20 m/s / 1.5 s
retardation = -13.33 m/s^2 (approximately)

So, the retardation of the car is approximately -13.33 m/s^2.

2. Calculating the time taken:
time = 2 * distance / (initial velocity + final velocity)

Plugging in the given values:
time = 2 * 30 m / (30 m/s + 10 m/s)

Simplifying:
time = 60 m / 40 m/s
time = 1.5 s

Therefore, it took the car 1.5 seconds to traverse the distance of 30 meters.

I will refrain from comment...

v^2 -vo^2 = 2ax
10^2 - 30^2 = 2*a*30.
Solve for a

v = vo + at so
t = v-vo/a using the a you just found.