a body moving with a uniform acceleration travels distance of 24m and 64m during the first two equal consecutive interval of time,each of duration 4s.determine the initial velocity and acceleration of the moving body
To determine the initial velocity and acceleration of the moving body, we can use the equations of motion.
Let's denote the initial velocity as 'u', the acceleration as 'a', and the time interval as 't'.
1. Distance traveled in the first interval:
Using the equation of motion, s = ut + (1/2)at^2, where s is the distance, u is the initial velocity, a is the acceleration, and t is the time.
In the first interval, the distance traveled is 24m, so we have:
24 = u(4) + (1/2)a(4)^2
2. Distance traveled in the second interval:
Again, using the equation of motion, s = ut + (1/2)at^2, but this time the distance is 64m, and the time is 2 times the duration of the first interval, which is 8s.
64 = u(8) + (1/2)a(8)^2
We now have two equations with two unknowns (u and a). Let's solve them simultaneously:
From equation (1):
24 = 4u + 8a (equation 3)
From equation (2):
64 = 8u + 32a (equation 4)
Multiplying equation (3) by 2, we get:
48 = 8u + 16a (equation 5)
Subtracting equation (5) from equation (4), we have:
64 - 48 = (8u + 32a) - (8u + 16a)
16 = 16a
a = 1 m/s^2
Substituting the value of 'a' back into equation (3):
24 = 4u + 8(1)
24 = 4u + 8
4u = 16
u = 4 m/s
Therefore, the initial velocity of the moving body is 4 m/s, and the acceleration is 1 m/s^2.