To find 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".
From the information given, we can identify two data points:
Data point 1: Time (t1) = 0 seconds (initial time) Displacement (s1) = 0 meters (initial displacement)
Data point 2: Time (t2) = 6 seconds Displacement (s2) = 25 meters
Using the equation for displacement:
s2 = s1 + u * t2 + 0.5 * a * t2^2
Substituting the known values:
25 = 0 + u * 6 + 0.5 * a * 6^2
Simplifying:
25 = 6u + 18a (Equation 1)
Next, we can use the second data point:
Data point 3: Time (t3) = 8 seconds Displacement (s3) = 45 meters
Again, using the equation for displacement:
s3 = s1 + u * t3 + 0.5 * a * t3^2
Substituting the known values:
45 = 0 + u * 8 + 0.5 * a * 8^2
Simplifying:
45 = 8u + 32a (Equation 2)
We now have a system of two equations (Equation 1 and Equation 2) with two variables (u and a). We can solve this system to find the values of u (initial velocity) and a (acceleration).
Solving the system of equations, we find: u = 4 m/s (initial velocity) a = 2 m/s^2 (acceleration)
Therefore, the initial velocity of the body is 4 m/s and the acceleration is 2 m/s^2.