Given:
- Displacement in the 3rd second = 1 m
- Displacement in the 10th second = 15 m

Assumptions:
- The body is moving in a straight line.
- The acceleration is constant.

Formula:
The displacement of an object with constant acceleration can be calculated using the formula:
s = ut + (1/2)at^2

Where:
s = displacement
u = initial velocity
t = time
a = acceleration

Solution:
Let's calculate the initial velocity of the body using the given information.

Step 1: Calculating acceleration:
To calculate the acceleration, we need to find the difference in displacement between the 10th second and the 3rd second, and the time difference between these two points.

Given:
Displacement in the 3rd second = 1 m
Displacement in the 10th second = 15 m

Using the formula for displacement, we have:
s = ut + (1/2)at^2

For the 3rd second:
1 = u(3) + (1/2)a(3)^2

For the 10th second:
15 = u(10) + (1/2)a(10)^2

Subtracting the equations, we get:
15 - 1 = u(10) - u(3) + (1/2)a(10)^2 - (1/2)a(3)^2
14 = u(10) - u(3) + (1/2)a(100) - (1/2)a(9)

Simplifying further:
14 = u(10) - u(3) + 50a - 4.5a
14 = u(10) - u(3) + 45.5a

Step 2: Calculating initial velocity:
To find the initial velocity, we need to substitute the values of displacements and the time interval into the displacement formula.

For the 3rd second:
1 = u(3) + (1/2)a(3)^2
1 = u(3) + (1/2)a(9)

For the 10th second:
15 = u(10) + (1/2)a(10)^2
15 = u(10) + (1/2)a(100)

Subtracting the equations, we get:
15 - 1 = u(10) - u(3) + (1/2)a(100) - (1/2)a(9)
14 = u(10) - u(3) + 50a - 4.5a
14 = u(10) - u(3) + 45.5a

Comparing the equations obtained in Step 1 and Step 2, we can equate the expressions for u(10) - u(3) + 45.5a:
u(10) - u(3) + 45.5a = u(10) - u(3) + 45.5a

Therefore, the initial velocity of the body is independent of the acceleration. We cannot determine the value of the initial velocity with the given information.