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.