To find the acceleration of the particle at a specific time, we first need to determine the position function, which is given as s(t) = t^2 + 4t + 4.
Next, we differentiate this position function to find the velocity of the particle with respect to time:
v(t) = s'(t) = 2t + 4
Now, we differentiate the velocity function to find the acceleration:
a(t) = v'(t) = 2
The acceleration, as we see, is constant and does not depend on time. Thus, regardless of the value of t, the acceleration is always 2.
Finally, substituting t = 4 into our acceleration function confirms this:
a(4) = 2
So, the acceleration of the particle when t = 4 is 2 units per second squared.