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Using the definition, calculate the derivative of the function. Then find the values of the derivative as specified.

User Cmani
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Final answer:

The acceleration is calculated by taking the derivative of the velocity function. The values of velocity and acceleration at a specific time are found by substituting that time into the respective functions. The direction of velocity and acceleration can be compared by observing their signs or values.

Step-by-step explanation:

(a) The acceleration is the derivative of the velocity function with respect to time. We take the derivative component by component:

a(t) = -16t + 48.

(b) To find the velocity at t = 3 seconds, we substitute t = 3 into the velocity function:

v(3) = -16(3) + 48 = 0.

(c) To find the acceleration at t = 3 seconds, we substitute t = 3 into the acceleration function:

a(3) = -16(3) + 48 = 0.

(d) Comparing the directions of velocity and acceleration at t = 3 seconds, we see that they both have zero values, which means they are in the same direction.

User Azuvector
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