Given:
The equation is given as S = 10t + 4t^2, where S represents the displacement and t represents time.

To find:
We need to find the acceleration, which represents the rate of change of velocity with respect to time.

Solution:

Step 1: Find the velocity:
To find the acceleration, we first need to find the velocity. Velocity is the rate of change of displacement with respect to time.

1. Differentiate the given equation S = 10t + 4t^2 with respect to time (t):
dS/dt = d(10t + 4t^2)/dt

2. Apply the power rule of differentiation:
dS/dt = 10 + 8t

3. The resulting expression represents the velocity (v) as a function of time.

Step 2: Find the acceleration:
Acceleration is the rate of change of velocity with respect to time.

1. Differentiate the velocity equation obtained in Step 1 with respect to time (t):
a = dv/dt = d(10 + 8t)/dt

2. Apply the power rule of differentiation:
a = 8

Step 3: Interpretation:
The acceleration, as obtained from the above calculations, is a constant value of 8. This means that the acceleration is not dependent on time and remains constant throughout the motion.

Summary:
The equation S = 10t + 4t^2 represents the displacement of an object as a function of time. By differentiating the equation twice, we find that the acceleration is a constant value of 8. This implies that the object is undergoing constant acceleration, regardless of the time elapsed.

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