the velocity acquired by a body moving with uniform acceleration is 12 m/s2 in 2 secs.and 18 m/s2 in 4 sec. find the initial velocity of the body?
vf=vi+at
Hmmm. I am wondering if you meant 12m/s and 18m/s. I will assume so.
12=vi+2a
18=vi+4a
subtract first from second equation
6=2a a=3 m/s^2
12=Vi+2*3 solve for vi
To find the initial velocity of the body, we can use the formula for velocity with uniform acceleration:
v = u + at
Where:
v = Final velocity
u = Initial velocity
a = Acceleration
t = Time taken
In the first scenario, the velocity acquired after 2 seconds is 12 m/s with an unknown initial velocity. Let's denote it as v1:
v1 = u + a * t1
Substituting in the given values:
12 m/s = u + a * 2 s
In the second scenario, the velocity acquired after 4 seconds is 18 m/s with an unknown initial velocity. Let's denote it as v2:
v2 = u + a * t2
Substituting in the given values:
18 m/s = u + a * 4 s
Now we have two equations with two unknowns (u and a). We can solve these equations simultaneously to find the initial velocity (u).
Let's solve the equation system:
12 m/s = u + a * 2 s [Equation 1]
18 m/s = u + a * 4 s [Equation 2]
Multiply Equation 1 by 2:
24 m/s = 2u + 4a [Equation 3]
Subtract Equation 2 from Equation 3:
6 m/s = 2a
Divide both sides by 2:
a = 3 m/s^2
Now, substitute the value of 'a' back into Equation 1:
12 m/s = u + 3 m/s^2 * 2 s
12 m/s = u + 6 m/s
Rearrange the equation to solve for 'u':
u = 12 m/s - 6 m/s
u = 6 m/s
Therefore, the initial velocity of the body is 6 m/s.