**Uniform Acceleration and Distance Travelled**

When a body moves with uniform acceleration, its velocity increases by the same amount in equal intervals of time. In this case, the distance travelled by the body in each second is given by the formula:

Sn = (0.4n + 9.8)m

Where Sn represents the distance travelled in the nth second.

**Finding Initial Velocity**

To find the initial velocity of the body, we need to determine the value of Sn for n = 1.

Substituting n = 1 into the formula, we get:

S1 = (0.4(1) + 9.8)m
S1 = (0.4 + 9.8)m
S1 = 10.2m

Therefore, the distance travelled in the first second is 10.2m.

**Understanding Distance Travelled**

We can observe that the distance travelled in each second is increasing by 0.4m. This suggests that the body is experiencing an acceleration of 0.4m/s^2.

In the first second, the body has covered a distance of 10.2m. We can calculate the average velocity for this interval using the formula:

Average Velocity = (Final Velocity + Initial Velocity) / 2

We know that the final velocity is the velocity at the end of the first second, which can be calculated using the formula:

Final Velocity = Initial Velocity + (Acceleration x Time)

Since the body is starting from rest, the initial velocity is 0. Therefore, the final velocity can be simplified to:

Final Velocity = 0 + (0.4 x 1)
Final Velocity = 0.4m/s

Now, we can calculate the average velocity:

Average Velocity = (0.4m/s + Initial Velocity) / 2
10.2m = (0.4m/s + Initial Velocity) / 2

Simplifying the equation, we get:

20.4m = 0.4m/s + Initial Velocity
Initial Velocity = 20.4m - 0.4m/s
Initial Velocity = 20m/s

Hence, the initial velocity of the body is 20m/s.

A stone is alowed to fall from top of a tower and covers half the height of the towel in the last sec of its journey.the time taken by stone to reach the foot of the tower is