Final answer:
The student's question pertains to the acceleration of a particle moving in a straight line with a given position function. Upon taking the first and second derivatives of the position function, it is determined that the acceleration is a constant 2 m/s², thus the acceleration at t = 4 is also 2 m/s².
Step-by-step explanation:
The student asks about the acceleration of a particle when its position function is given by S(t) = t² + 4t + 4. To find the acceleration, we need to apply calculus and find the second derivative of the position function with respect to time, since acceleration is the second derivative of position with respect to time.
The position function S(t) can be differentiated to get the velocity function, and then the velocity function can be differentiated to get the acceleration function:
- First derivative (velocity): V(t) = dS(t)/dt = 2t + 4
- Second derivative (acceleration): A(t) = dV(t)/dt = d2S(t)/dt2 = 2
The acceleration is a constant value of 2 m/s², so the acceleration of the particle when t = 4 is also 2 m/s².