The velocity acquired by a body moving with uniform acceleration is 12m/s in 2 seconds and 18m/s in 4 seconds.Find the initial velocity of the body.

it gained (18-12)=6 m/s in (4-2)=2 seconds, so that is

6/2 = 3 m/s^2

In the first 2 seconds, then, it gained 6 m/s, so it started at 6 m/s.

To find the initial velocity of the body, we can use the equations of motion. The equation that relates velocity, acceleration, and time is:

v = u + at

where:
- v is the final velocity
- u is the initial velocity
- a is the acceleration
- t is the time

We are given two sets of information:
1. The velocity acquired in 2 seconds is 12 m/s.
2. The velocity acquired in 4 seconds is 18 m/s.

Let's solve this step by step:

Step 1: Using the first set of information (v = 12 m/s, t = 2 s), we can substitute these values into the equation:

12 = u + a * 2

Step 2: Using the second set of information (v = 18 m/s, t = 4 s), we can substitute these values into the equation:

18 = u + a * 4

Step 3: Now we have a system of two equations with two variables (u and a). We can solve these simultaneously to find the values of u and a.

Solving the equations:

From equation 1 (12 = u + a * 2), we can rewrite it as:

u = 12 - 2a

Substituting this value of u into equation 2 (18 = u + a * 4):

18 = (12 - 2a) + a * 4

Step 4: Simplify and solve for a:

18 = 12 - 2a + 4a
18 = 12 + 2a
6 = 2a
a = 6/2
a = 3 m/s^2

Step 5: Now that we have the value of acceleration (a = 3 m/s^2), we can substitute this back into equation 1 (12 = u + a * 2):

12 = u + 3 * 2
12 = u + 6
u = 12 - 6
u = 6 m/s

Therefore, the initial velocity of the body is 6 m/s.