To determine the velocity of the particle at t = 4.0 s, we need to calculate the acceleration at that time and then use it to find the final velocity.
The given formula for acceleration is correct:
a = force / mass = (3t^2 - 12t) / 4
Now, let's substitute t = 4.0 s into the equation to find the acceleration at t = 4.0 s:
a(4) = (3(4)^2 - 12(4)) / 4
= (3(16) - 48) / 4
= (48 - 48) / 4
= 0 / 4
= 0 m/s^2
So, you are correct in calculating the acceleration at t = 4.0 s as 0 m/s^2.
To determine the final velocity v(4), we can use the kinematic equation:
v(4) = v(0) + a * t
Given that the initial velocity v(0) is -6.0 m/s and the acceleration a(4) is 0 m/s^2, we substitute these values into the equation:
v(4) = -6.0 m/s + 0 m/s^2 * 4.0 s
= -6.0 m/s
Hence, the velocity of the particle at t = 4.0 s is -6.0 m/s.