To determine the initial velocity and acceleration of the body, we can use the kinematic equations of motion. Let's denote the initial velocity as "u" and the acceleration as "a."
The first equation relates displacement, initial velocity, time, and acceleration:
s = ut + (1/2)at^2,
where s is the displacement, t is the time, and u and a are the unknowns.
From the given information, we can set up two equations:
Equation 1: 25 = u(6) + (1/2)a(6)^2, Equation 2: 45 = u(8) + (1/2)a(8)^2.
We can solve this system of equations to find the values of u and a.
Let's start by simplifying the equations:
- 25 = 6u + 18a,
- 45 = 8u + 32a.
To eliminate u, we'll multiply Equation 1 by 4 and Equation 2 by 3:
- 100 = 24u + 72a,
- 135 = 24u + 96a.
Now, we'll subtract Equation 3 from Equation 4:
135 - 100 = 24u + 96a - 24u - 72a, 35 = 24a.
Dividing both sides by 24, we find:
a = 35/24.
Now we can substitute this value of "a" into Equation 1 to solve for "u":
25 = 6u + (1/2)(35/24)(6)^2.
Simplifying further:
25 = 6u + (35/4)(6).
25 = 6u + (35/4)(6).
Multiplying 35/4 by 6:
25 = 6u + 35/4 * 6 = 6u + 35/2.
Now, we'll isolate "u" by moving the terms around:
25 - 35/2 = 6u,
50/2 - 35/2 = 6u,
15/2 = 6u,
Dividing both sides by 6:
15/12 = u,
5/4 = u.
Therefore, the initial velocity (u) of the body is 5/4 m/s, and the acceleration (a) is 35/24 m/s^2.