## Answer :

1.

**Find the Velocity Function**:

The velocity function is the first derivative of the position function with respect to time [tex]\( t \)[/tex].

[tex]\[ v(t) = \frac{d}{dt}[2t^3 + 2t^2 + 5t - 20] \][/tex]

Taking the derivative:

[tex]\[ v(t) = 6t^2 + 4t + 5 \, \text{m/s} \][/tex]

2.

**Find the Acceleration Function**:

The acceleration function is the first derivative of the velocity function, which means it is the second derivative of the position function.

[tex]\[ a(t) = \frac{d}{dt}[6t^2 + 4t + 5] \][/tex]

Taking the derivative:

[tex]\[ a(t) = 12t + 4 \, \text{m/s}^2 \][/tex]

3.

**Evaluate the Acceleration at [tex]\( t = 2 \)[/tex]**:

Substitute [tex]\( t = 2 \)[/tex] into the acceleration function:

[tex]\[ a(2) = 12(2) + 4 \][/tex]

Simplifying this:

[tex]\[ a(2) = 24 + 4 = 28 \, \text{m/s}^2 \][/tex]

Thus, the acceleration at [tex]\( t = 2 \)[/tex] is [tex]\( 28 \, \text{m/s}^2 \)[/tex].

Based on the provided options, the correct answer is:

(C) [tex]\( 28 \, \text{m/s}^2 \)[/tex]