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.