**Finding Retardation in Motion: Formula and Explanation**

Motion is the change in position of an object with respect to time. When an object is slowing down or decelerating, it is said to be experiencing retardation. Retardation is the negative acceleration of an object in motion. It can be calculated using the formula:

**Retardation (a) = (Final Velocity (v) - Initial Velocity (u)) / Time (t)**

Let's break down the formula and explain each component in detail.

1. **Final Velocity (v):** This refers to the velocity of the object at the end of the time period under consideration. It is usually denoted by 'v' in the formula.

2. **Initial Velocity (u):** This represents the velocity of the object at the beginning of the time period under consideration. It is usually denoted by 'u' in the formula.

3. **Time (t):** This is the duration of the motion or the time interval during which the change in velocity occurs. It is denoted by 't' in the formula.

By subtracting the initial velocity from the final velocity and then dividing it by the time taken, we obtain the retardation. The unit of retardation is the same as that of acceleration, which is meters per second squared (m/s²) in the SI system.

**Example Numerical:**

Let's consider an example to understand how to calculate retardation using the formula.

**Question:** An object starts from rest and comes to a halt in 10 seconds with a velocity of 30 m/s. Calculate the retardation.

**Solution:**

Given:
Initial velocity (u) = 0 m/s (since the object starts from rest)
Final velocity (v) = 30 m/s
Time (t) = 10 s

Using the formula:
Retardation (a) = (v - u) / t
= (30 - 0) / 10
= 30 / 10
= 3 m/s²

Therefore, the retardation of the object in this example is 3 m/s².

In conclusion, retardation in motion can be calculated using the formula (v - u) / t, where 'v' is the final velocity, 'u' is the initial velocity, and 't' is the time taken. By substituting the appropriate values into the formula, we can determine the retardation of an object.

By using the formulae
a=v-u/t
v=final velocity
u=initial velocityt=time
a=acceleration
if a is negative then it will be retardation