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

V increases by 6 m/s every 2 seconds. The acceleration is therefore 6/2 = 3 m/s^2.

If V = 12 m/s at t = 2, then V = 6 m/s at t = 0.

V(t) = Vo + a*t = 6 + 3*t

To find the initial velocity (u) of the body, we can use the equation of motion:

v = u + at

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

Given that the final velocity at 2 seconds is 12 m/s and at 4 seconds is 18 m/s, we can set up two equations:

12 = u + a(2)
18 = u + a(4)

We have two equations with two unknowns (u and a). To solve this system of equations, we can use a method called elimination.

First, let's solve for a by eliminating u. Multiply the first equation by 2 to eliminate u:

24 = 2u + 2a

Now we can subtract this equation from the second equation to eliminate u:

18 = (u + 2a) - (2u + 2a)
18 = -u
u = -18

The initial velocity of the body is -18 m/s. However, velocity cannot be negative in this context, so it is impossible for the body to have a negative initial velocity. This means there might be an error in the given information or the question itself.